From 8992f1b92f22d3229f003148619f7c2c6e2c7a26 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 15 Apr 2019 22:39:32 -0400
Subject: [PATCH 01/55] Added decoding example of Hello World

Under tests section:

> Example Test string encoding:

- Decode Target: `hello world

- Each letter decodes to respective 6-bit group: `"010001","001110","010101","010101","011000"," ", "100000","011000","011011","010101","001101",

- Each Word as Continous string `"010001001110010101010101011000" "100000011000011011010101001101"

- Concatenation of both words into one string: `"010001001110010101010101011000100000011000011011010101001101"

- Converted binary string to hex: `0x44e55562061b54d`
---
 README.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/README.md b/README.md
index 3c3632f..1e5088f 100644
--- a/README.md
+++ b/README.md
@@ -174,6 +174,18 @@ Python 3 or higher
 
 ## Tests: 
 
+> Example Test string encoding:
+
+- Decode Target: `hello world
+
+- Each letter decodes to respective 6-bit group: `"010001","001110","010101","010101","011000"," ", "100000","011000","011011","010101","001101",
+
+- Each Word as Continous string `"010001001110010101010101011000" "100000011000011011010101001101"
+
+- Concatenation of both words into one string: `"010001001110010101010101011000100000011000011011010101001101"
+
+- Converted binary string to hex: `0x44e55562061b54d`
+
 ## Reources: 
 
 ## Roadmap/Plans:

From 136976b9a632b399a49f8eea02ff476bc892f35c Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 11:11:37 -0400
Subject: [PATCH 02/55] Update README.md

---
 README.md | 23 +++++++++++++----------
 1 file changed, 13 insertions(+), 10 deletions(-)

diff --git a/README.md b/README.md
index 1e5088f..9024c86 100644
--- a/README.md
+++ b/README.md
@@ -1,9 +1,9 @@
 # Hatnotation
 
-> Hatnotation is short for the *Hatzakis Base 64 notation system* which is a method to encode/decode arbitrary binary strings of data, invented by Steven Hatzakis and open-sourced here under Apache License 2.0 https://github.com/hatgit/hatnotation/blob/master/LICENSE.
+> Hatnotation is short for the *Hatzakis Base 64 notation system* which is a method to encode/decode arbitrary binary strings of data, invented by Steven Hatzakis and open-sourced here under [Apache License 2.0](https://github.com/hatgit/hatnotation/blob/master/LICENSE).
 
  <blockquote>
-<pre><code>[Use of Hatnotation is subject to Apache License 2.0 ] <a href="https://github.com/hatgit/hatnotation/blob/master/LICENSE">https://github.com/hatgit/hatnotation/blob/master/LICENSE</a>
+<pre><code>[Use of Hatnotation is subject to Apache License 2.0] <a href="https://github.com/hatgit/hatnotation/blob/master/LICENSE">https://github.com/hatgit/hatnotation/blob/master/LICENSE</a>
 </code></pre>
 </blockquote>
 
@@ -17,7 +17,7 @@ This software is still in its experimental phase and should not be relied upon f
 
 ## Background on Mnemonics (private keys) and Human vs Machine-readable code
 
-Mnemonics (aka recovery phrases) are used in many popular crypto wallet applciations including BIP39 (which follows a specific wordlist and checksum requirement, among other steps for wallet derivation such as BIP32, BIP44) enable a user to backup their initial entropy in human-readable format. 
+Mnemonics (aka recovery phrases) are used in many popular crypto wallet applciations including [BIP39 (https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki) (which follows a specific wordlist and checksum requirement, among other steps for wallet derivation such as BIP32, BIP44) enable a user to backup their initial entropy in human-readable format. 
 
 For example, instead of a user having to backup a string of 128 bits or their private key, they can simply store the encoded mnemonic which represents those bits or a private key. 
 
@@ -32,7 +32,7 @@ For example, instead of a user having to backup a string of 128 bits or their pr
 |Total Words     |`132/11 = 12 words`            |`264/11 = 24 words`          |
 |----------------|-------------------------------|-----------------------------|
 
-In terms of actual pre-image resistance, the initial entropy should be generated in a cryptographically-secure manner that is pre-image resistant and resistant to other attacks, such as outlined in the W3C Cryptography API or via the "secrets" module in Python), and the psuedo-random binary string that results will be that is machine-readable where the purpose of encoding it into a mnemonic is to make it easier to notate, recite, read, and write, compared to binary (machine-readable).
+In terms of actual pre-image resistance, the initial entropy should be generated in a cryptographically-secure manner that is pre-image resistant and resistant to other attacks, such as outlined in the [W3C Cryptography API](https://www.w3.org/TR/WebCryptoAPI/) or via the [secrets](https://docs.python.org/3/library/secrets.html) module in Python), and the psuedo-random binary string that results will be machine-readable where the purpose of encoding it into a mnemonic is to make it easier to notate, recite, read, and write, (i.e. human-readable) compared to binary (machine-readable).
 
 
 
@@ -62,15 +62,18 @@ The Hatnotation system is *not intended to be an alternative to human-readable m
 Just as a mnemonic that represents a 132 bits of some initial entropy should convey 128 bits of security if generated properly, as the last 4 bits are deterministically derived from the hash-based checksum computation (hashing the initial entropy as a byte array). Those same 132 bits can be encoded using the Hatnotation system which will result in 22 characters, sourced from the 64 character library. Mathematically, 64^22 == 2^132, hence why there is no information/security loss, for example. 
 
 ### Lemma 
-For any arbitrary binary (base-2) string x of length n, after hatnotation is applied to x, the length n = ((x - (x % 6))/6)+(x %6, optionally in some cases depending on how the encoder/decoder is constructed). Optimal compression will occur when the [COMPLETE THIS SECTION]  
+For any arbitrary binary (base-2) string x of length n, after hatnotation is applied to x, the length n = ((x - (x % 6))/6)+(x %6, optionally in some cases depending on how the encoder/decoder is constructed). 
 
-- `(128-(128 % 6)) / 6 == 21 == 2^128`
-- `(132-(132 % 6)) / 6 == 22 == 2^132`
-- `(256-(256 % 6)) / 6 == 42 == 2^256`
-- `(264-(264 % 6)) / 6 == 44 == 2^264`
+Optimal compression will occur when the x modulo 6 is equal to zero, and least optimum when x modulo 6 is equal to 5 (The assumption in this last sentence should be checked). 
 
+Below are two examples of when notation is optimum, using 132 bits and 264 bits as an example, and which are standard bit-lengths for the underlying entropy that represents 12-word or 24-word mnemonics used with crypto wallets. 
 
-|  Private Key          |12-word mnemonic               |24-word mnemonic     |
+- `(64^((132-(132 % 6)) / 6) == 2^132`
+
+- `(64^((264-(264 % 6)) / 6) == 2^264`
+
+
+|  Private Key          |Length after Hatnotation     | BIP39 checksum    |
 |----------------|-------------------------------|-----------------------------|
 | 128 bits       |21 characters                |Checksum must be computed  |
 | 132 bits       |22 characters             |Checksum included     |

From c98db0b9bfa8801b256e9f585e87e9891dfaab7d Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 11:12:02 -0400
Subject: [PATCH 03/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 9024c86..a118590 100644
--- a/README.md
+++ b/README.md
@@ -8,7 +8,7 @@
 </blockquote>
 
 ## Purpose
-An encoding/decoding method that allows users to compress their human-readable data into fewer humand-readable characters than other popular notation systems, for any arbitrary underlying machine-readable binary string. 
+An encoding/decoding method that allows users to compress their human-readable data into fewer human-readable characters than other popular notation systems, for any arbitrary underlying machine-readable binary string. 
 
 
 ## Warning: 

From e6cebd7f48c471072e0aeb236fac8fdbbbc9b75a Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 11:15:10 -0400
Subject: [PATCH 04/55] Update README.md

---
 README.md | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index a118590..0ed8ffa 100644
--- a/README.md
+++ b/README.md
@@ -177,9 +177,9 @@ Python 3 or higher
 
 ## Tests: 
 
-> Example Test string encoding:
+> Example Test strings: 
 
-- Decode Target: `hello world
+- Decode Target: `helloworld
 
 - Each letter decodes to respective 6-bit group: `"010001","001110","010101","010101","011000"," ", "100000","011000","011011","010101","001101",
 
@@ -187,10 +187,13 @@ Python 3 or higher
 
 - Concatenation of both words into one string: `"010001001110010101010101011000100000011000011011010101001101"
 
-- Converted binary string to hex: `0x44e55562061b54d`
+- Converted binary string to hex (can be used as starting point to encode to "helloworld": `0x44e55562061b54d`
 
 ## Reources: 
 
+-Other base64 encoding schemes: https://en.wikipedia.org/wiki/Base64
+-Notational conventions: https://tools.ietf.org/html/rfc2822
+
 ## Roadmap/Plans:
 
 

From 661a2091e286bfd2e231e9893a90d566b1a7b181 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 11:29:17 -0400
Subject: [PATCH 05/55] Update README.md

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 0ed8ffa..13b10e4 100644
--- a/README.md
+++ b/README.md
@@ -191,8 +191,8 @@ Python 3 or higher
 
 ## Reources: 
 
--Other base64 encoding schemes: https://en.wikipedia.org/wiki/Base64
--Notational conventions: https://tools.ietf.org/html/rfc2822
+- Other base64 encoding schemes: https://en.wikipedia.org/wiki/Base64
+- Notational conventions: https://tools.ietf.org/html/rfc2822
 
 ## Roadmap/Plans:
 

From ae43bf4863046efe3dd6c9ba3c1dbc36c16181f6 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 11:36:44 -0400
Subject: [PATCH 06/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 13b10e4..1b86fb8 100644
--- a/README.md
+++ b/README.md
@@ -189,7 +189,7 @@ Python 3 or higher
 
 - Converted binary string to hex (can be used as starting point to encode to "helloworld": `0x44e55562061b54d`
 
-## Reources: 
+## Resources: 
 
 - Other base64 encoding schemes: https://en.wikipedia.org/wiki/Base64
 - Notational conventions: https://tools.ietf.org/html/rfc2822

From ce54ae34dfaf0656d2fc33c15b7006a912b7baea Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 13:01:41 -0400
Subject: [PATCH 07/55] Fix backslash at index 59 in library not rendering

the `\` character wasn't rendering in markup here and also may be an issue to look at in Python decoder.
---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1b86fb8..0aaad27 100644
--- a/README.md
+++ b/README.md
@@ -151,7 +151,7 @@ Using the binascii libary in python which contains the string library, we source
 56 | "111000", | "?",
 57 | "111001", | "@",
 58 | "111010", | "[",
-59 | "111011", | "\",
+59 | "111011", | "\\",
 60 | "111100", | "]",
 61 | "111101", | "^",
 62 | "111110", | "_",

From 379197e06b2d2e2569f4ad2d2d92cd89c03232a1 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 13:45:01 -0400
Subject: [PATCH 08/55] Update README.md

---
 README.md | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/README.md b/README.md
index 0aaad27..0afd71a 100644
--- a/README.md
+++ b/README.md
@@ -189,6 +189,10 @@ Python 3 or higher
 
 - Converted binary string to hex (can be used as starting point to encode to "helloworld": `0x44e55562061b54d`
 
+
+Second Test: Decoder should be able to take a single backslash `\` and return index value 59, as well as multiple ones '`\\\\\`' and not be affected by any formatting/rendering issues of the app or interface (i.e. python or javascript/html).
+
+
 ## Resources: 
 
 - Other base64 encoding schemes: https://en.wikipedia.org/wiki/Base64
@@ -196,4 +200,6 @@ Python 3 or higher
 
 ## Roadmap/Plans:
 
+- develop a range of potential use cases 
+- potentially propose a request for comments (RFC) for consideration as a standard.
 

From cf9a5d4822e66c2b7e750ad86d1b840ab562ab41 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 16 Apr 2019 15:45:40 -0400
Subject: [PATCH 09/55] Update README.md

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 0afd71a..9a45d31 100644
--- a/README.md
+++ b/README.md
@@ -197,6 +197,7 @@ Second Test: Decoder should be able to take a single backslash `\` and return in
 
 - Other base64 encoding schemes: https://en.wikipedia.org/wiki/Base64
 - Notational conventions: https://tools.ietf.org/html/rfc2822
+- Human-readable keys (1994) https://tools.ietf.org/html/rfc1751
 
 ## Roadmap/Plans:
 

From 3f0b0fdf15f326d29103ba043410576f44ab9178 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Wed, 17 Apr 2019 01:17:41 -0400
Subject: [PATCH 10/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 9a45d31..7745ba4 100644
--- a/README.md
+++ b/README.md
@@ -13,7 +13,7 @@ An encoding/decoding method that allows users to compress their human-readable d
 
 ## Warning: 
 
-This software is still in its experimental phase and should not be relied upon for production. 
+This software is still in its experimental phase and should not be relied upon for production.  
 
 ## Background on Mnemonics (private keys) and Human vs Machine-readable code
 

From bab9cd7b6719d6de38253c9f674361722bf224f4 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Wed, 17 Apr 2019 23:01:35 -0400
Subject: [PATCH 11/55] Updated library with new characters and added note

the backslash `\` and forwadslash `/`characters were swapped with opening `{` and closing `}` curly brackets in the following issue: https://github.com/hatgit/hatnotation/issues/3
---
 README.md | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index 7745ba4..4fea1a6 100644
--- a/README.md
+++ b/README.md
@@ -142,7 +142,7 @@ Using the binascii libary in python which contains the string library, we source
 47 | "101111", | ",",
 48 | "110000", | "-",
 49 | "110001", | ".",
-50 | "110010", | "/",
+50 | "110010", | "{",
 51 | "110011", | ":",
 52 | "110100", | ";",
 53 | "110101", | "<",
@@ -151,7 +151,7 @@ Using the binascii libary in python which contains the string library, we source
 56 | "111000", | "?",
 57 | "111001", | "@",
 58 | "111010", | "[",
-59 | "111011", | "\\",
+59 | "111011", | "}",
 60 | "111100", | "]",
 61 | "111101", | "^",
 62 | "111110", | "_",
@@ -159,14 +159,17 @@ Using the binascii libary in python which contains the string library, we source
 
 ## Library verification
 
-In Python version 3.7 using the strings library, the following steps can be taken to verify the library and character order and by omitting the last 4 characters "{|}~" in the fourth step below (zeroed-index values 64-67 which have been omitted from the above list as well): 
+In Python version 3.7 using the strings library, the following steps can be taken to verify the library and character order and notice that the following 4 characters are omitted "\\~/|" in the fourth step below: 
 
 - ```>>> import string```
 - ```>>> dir(string)['Formatter', 'Template', '_ChainMap', '_TemplateMetaclass', '__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '_re', '_string', 'ascii_letters', 'ascii_lowercase', 'ascii_uppercase', 'capwords', 'digits', 'hexdigits', 'octdigits', 'printable', 'punctuation', 'whitespace']```
 - ```>>> print(string.digits+string.ascii_uppercase+string.punctuation)```
 - ```0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-./:;<=>?@[\]^_`{|}~```
 
-(i.e. ~~```"{|}~"```~~)
+- Note, the backslash `\` and forwadslash `/`characters were swapped with opening `{` and closing `}` curly brackets in the following issue: https://github.com/hatgit/hatnotation/issues/3. 
+- The list of valid Hatnotation library characters are thus as follows: ```0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_````
+
+(and the following four remain excluded/reserved ~~```"\/|~"```~~).
 
 ## Requirements
 
@@ -179,7 +182,7 @@ Python 3 or higher
 
 > Example Test strings: 
 
-- Decode Target: `helloworld
+- Decode Target: `HELLOWORLD
 
 - Each letter decodes to respective 6-bit group: `"010001","001110","010101","010101","011000"," ", "100000","011000","011011","010101","001101",
 
@@ -203,4 +206,5 @@ Second Test: Decoder should be able to take a single backslash `\` and return in
 
 - develop a range of potential use cases 
 - potentially propose a request for comments (RFC) for consideration as a standard.
+- add error message for invalid characters (i.e. lowercase and reserved characters `\|/~`
 

From 2475c93bd0d40e567869d256d9fd833ca4e1ad8a Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Wed, 17 Apr 2019 23:01:56 -0400
Subject: [PATCH 12/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 4fea1a6..59e95bb 100644
--- a/README.md
+++ b/README.md
@@ -166,7 +166,7 @@ In Python version 3.7 using the strings library, the following steps can be take
 - ```>>> print(string.digits+string.ascii_uppercase+string.punctuation)```
 - ```0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-./:;<=>?@[\]^_`{|}~```
 
-- Note, the backslash `\` and forwadslash `/`characters were swapped with opening `{` and closing `}` curly brackets in the following issue: https://github.com/hatgit/hatnotation/issues/3. 
+- Note, the backslash `\` and forwardslash `/`characters were swapped with opening `{` and closing `}` curly brackets in the following issue: https://github.com/hatgit/hatnotation/issues/3. 
 - The list of valid Hatnotation library characters are thus as follows: ```0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_````
 
 (and the following four remain excluded/reserved ~~```"\/|~"```~~).

From 9c16abcbafc3a60dbd2cf749dfceda9b0a9ba153 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Wed, 17 Apr 2019 23:11:26 -0400
Subject: [PATCH 13/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 59e95bb..858106a 100644
--- a/README.md
+++ b/README.md
@@ -167,7 +167,7 @@ In Python version 3.7 using the strings library, the following steps can be take
 - ```0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-./:;<=>?@[\]^_`{|}~```
 
 - Note, the backslash `\` and forwardslash `/`characters were swapped with opening `{` and closing `}` curly brackets in the following issue: https://github.com/hatgit/hatnotation/issues/3. 
-- The list of valid Hatnotation library characters are thus as follows: ```0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_````
+- The list of valid Hatnotation library characters are thus as follows: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_`
 
 (and the following four remain excluded/reserved ~~```"\/|~"```~~).
 

From 9504bbc563a487849e59e8ceacd9982269a01d0b Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 18 Apr 2019 21:19:34 -0400
Subject: [PATCH 14/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 858106a..7f6ea43 100644
--- a/README.md
+++ b/README.md
@@ -21,7 +21,7 @@ Mnemonics (aka recovery phrases) are used in many popular crypto wallet applciat
 
 For example, instead of a user having to backup a string of 128 bits or their private key, they can simply store the encoded mnemonic which represents those bits or a private key. 
 
-> Note: While the word "private key" is usually associated with public/private key-pairs in cryptogrpahy, for the purpose of this Readme.md file, the use of private key refers to the master private key (initial entropy) for a crypto vault (within which accounts and private keys are dervived) which can also be considered a pre-image of the mnemonic.
+> Note: While the word "private key" is usually associated with public/private key-pairs in cryptogrpahy, for the purpose of this Readme.md file, the use of private key refers to the master private key (initial entropy) for a crypto vault (within which accounts and private keys are derived) which can also be considered a pre-image of the mnemonic.
 
 
 |                |12-word mnemonic               |24-word mnemonic             |

From 4d7d6918a681f7cf9154474dbc6732313b6a2725 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 18 Apr 2019 21:22:40 -0400
Subject: [PATCH 15/55] Update README.md

---
 README.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/README.md b/README.md
index 7f6ea43..5568630 100644
--- a/README.md
+++ b/README.md
@@ -193,8 +193,6 @@ Python 3 or higher
 - Converted binary string to hex (can be used as starting point to encode to "helloworld": `0x44e55562061b54d`
 
 
-Second Test: Decoder should be able to take a single backslash `\` and return index value 59, as well as multiple ones '`\\\\\`' and not be affected by any formatting/rendering issues of the app or interface (i.e. python or javascript/html).
-
 
 ## Resources: 
 

From 66727918cef8a5bdfad21051d52b9c1e483c7fbc Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 25 Apr 2019 11:51:46 -0400
Subject: [PATCH 16/55] corrected formatting of message so that "'" shows

On the line: hatdata2decode=input
The formatting of the string was corrected thanks to a fix by @PumpkingWok
---
 base64Decode_v1_01.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base64Decode_v1_01.py b/base64Decode_v1_01.py
index 16ee090..d145f3c 100644
--- a/base64Decode_v1_01.py
+++ b/base64Decode_v1_01.py
@@ -101,7 +101,7 @@ def decodeAsHex(string):
 
     return hex(int(decodeAsBin(string), 2))
 
-hatdata2decode=input('Enter any combination of the following characters to decode without spaces: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&''()*+,-.{:;<=>?@[}]^_`":')
+hatdata2decode=input('Enter any combination of the following characters to decode without spaces: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"'"#$%&'"'()*+,-.{:;<=>?@[}]^_`:')
                      
 print(decodeAsBin(hatdata2decode))
 

From 0aebb891b95cc601601d0cd0a9a5e71ad6fc9f88 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 25 Apr 2019 17:46:03 -0400
Subject: [PATCH 17/55] fixed "+" to '+' to avoid print formatting issues

---
 base64Decode_v1_01.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base64Decode_v1_01.py b/base64Decode_v1_01.py
index d145f3c..e3bb203 100644
--- a/base64Decode_v1_01.py
+++ b/base64Decode_v1_01.py
@@ -63,7 +63,7 @@
 "(",
 ")",
 "*",
-"+",
+'+',
 ",",
 "-",
 ".",

From 61ccac1170f5737027cb612225a5b96cecddf5ca Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 25 Apr 2019 17:49:20 -0400
Subject: [PATCH 18/55] fixed "+" to '+' to avoid format issues printing

---
 base64encode_v1_01.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base64encode_v1_01.py b/base64encode_v1_01.py
index 3363b34..28f7e78 100644
--- a/base64encode_v1_01.py
+++ b/base64encode_v1_01.py
@@ -65,7 +65,7 @@ def base64en(address_hex):   # important never to rename base64en to "base64" wh
 "(",
 ")",
 "*",
-"+",
+'+',
 ",",
 "-",
 ".",

From 90da18094347ad3610c65e4c5c0ed7f916633995 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 25 Apr 2019 17:51:14 -0400
Subject: [PATCH 19/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 5568630..75661d0 100644
--- a/README.md
+++ b/README.md
@@ -138,7 +138,7 @@ Using the binascii libary in python which contains the string library, we source
 43 | "101011", | "(",
 44 | "101100", | ")",
 45 | "101101", | "*",
-46 | "101110", | "+",
+46 | "101110", | '+',
 47 | "101111", | ",",
 48 | "110000", | "-",
 49 | "110001", | ".",

From 937ca794a313870ecce8229054e799533c5dd95b Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Thu, 25 Apr 2019 17:53:02 -0400
Subject: [PATCH 20/55] Update README.md

---
 README.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/README.md b/README.md
index 75661d0..ee8da47 100644
--- a/README.md
+++ b/README.md
@@ -171,6 +171,13 @@ In Python version 3.7 using the strings library, the following steps can be take
 
 (and the following four remain excluded/reserved ~~```"\/|~"```~~).
 
+
+The following Hex string can be fed to the encoder to print all characters in order except for the first which is "0" (zero) and gets omitted: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
+
+The loss of leading zeroes has been discussed in the following issue and is common across notation systems when converting from padded binary data: https://github.com/hatgit/hatnotation/issues/6
+
+** There can be some formatting issues in Python which affect how data is printed as noted in this committ: https://github.com/hatgit/hatnotation/commit/66727918cef8a5bdfad21051d52b9c1e483c7fbc
+
 ## Requirements
 
 Python 3 or higher

From 3f3246ab9056b82214631d8be5dcf19acd453a8b Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Fri, 26 Apr 2019 22:43:10 -0400
Subject: [PATCH 21/55] Update README.md

Added hat emoji to H1
---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ee8da47..215466a 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,4 @@
-# Hatnotation
+# :tophat: Hatnotation
 
 > Hatnotation is short for the *Hatzakis Base 64 notation system* which is a method to encode/decode arbitrary binary strings of data, invented by Steven Hatzakis and open-sourced here under [Apache License 2.0](https://github.com/hatgit/hatnotation/blob/master/LICENSE).
 

From 80a13fb773321c41bec831b1b349044321962e20 Mon Sep 17 00:00:00 2001
From: andrea zuccarini <andrearanma@gmail.com>
Date: Sat, 27 Apr 2019 12:16:13 +0200
Subject: [PATCH 22/55] add decode js file

---
 base64Decode_v1_01.js | 125 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 125 insertions(+)
 create mode 100644 base64Decode_v1_01.js

diff --git a/base64Decode_v1_01.js b/base64Decode_v1_01.js
new file mode 100644
index 0000000..95b8fc0
--- /dev/null
+++ b/base64Decode_v1_01.js
@@ -0,0 +1,125 @@
+//Author: Andrea Zuccarini @2019
+
+//Version 1.01
+
+// Example Test string target to decode: HELLOWORLD
+// Each letter decodes to respective 6-bit group: "010001","001110","010101","010101","011000"," ", "100000","011000","011011","010101","001101",
+// Each Word as Continous string "010001001110010101010101011000" "100000011000011011010101001101"
+// Concatenation of both words into one string: "010001001110010101010101011000100000011000011011010101001101"
+// Converted binary string to hex: "0x44e55562061b54d"
+
+
+b64dict= {};
+
+base64library=['0',
+'1',
+'2',
+'3',
+'4',
+'5',
+'6',
+'7',
+'8',
+'9',
+'A',
+'B',
+'C',
+'D',
+"E",
+'F',
+'G',
+'H',
+'I',
+'J',
+'K',
+'L',
+'M',
+'N',
+'O',
+'P',
+'Q',
+'R',
+'S',
+'T',
+'U',
+'V',
+'W',
+'X',
+'Y',
+'Z',
+'!',
+'"',
+'#',
+'$',
+'%',
+'&',
+"'",
+'(',
+')',
+'*',
+'+',
+',',
+'-',
+'.',
+'}',
+':',
+';',
+'<',
+'=',
+'>',
+'?',
+'@',
+'[',
+'{',
+']',
+'^',
+'_',
+'`'];
+
+for(var i=0;i<base64library.length;i++) {
+    b64dict[base64library[i]] = i;
+}
+
+function zfill(source, length) {
+  var source = source.toString();
+  while(source.length < length) {
+    source = '0' + source;
+  }
+  return source;
+}
+
+function decodeAsBin(string) {
+    output = [];
+    s='';
+    for(var j=0;j<string.length;j++) {
+      if(string[j] != ' ') {
+        output.push(zfill(b64dict[string[j].toUpperCase()].toString(2), 6));
+      }
+    }
+    return output.join('');
+}
+
+function decodeAsHex(string) {
+  bin = decodeAsBin(string);
+  output = [];
+  s='';
+  // Pad with 0 for binaries not divisible by 4, for hex conversion
+  binModule = bin.length % 4;
+  if(binModule != 0) {
+    bin = zfill(bin, bin.length + 4 - binModule);
+  }
+  for(var i=0;i<bin.length;i=i+4) {
+    output.push(parseInt(bin.slice(i,i+4), 2).toString(16));
+  }
+  return output.join('');
+}
+
+//hatdata2decode=prompt('Enter any combination of the following characters to decode without spaces: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&()*+,-.{:;<=>?@[}]^_`:');
+console.log(decodeAsBin('HELLOWORLD'));
+console.log('0x' + decodeAsHex('HELLOWORLD'));
+
+
+// test decode string "HELLOWORLD" should return the binary equivalent of hex: 0x44e55562061b54d
+// test decode string "INVENTEDBYSTEVENHATZAKIS@2018" should return this hex 0x125df39774e34b89c74e7ce5d129d8ca512739080048 as equivalent in binary to this output: 010010010111011111001110010111011101001110001101001011100010011100011101001110011111001110010111010001001010011101100011001010010100010010011100111001000010000000000001001000
+
+// Note/CONSIDERATION: In version 1.01 to resolve a rendering conflict, the Forward slash "/" and Backslash "\" characters have been swapped out and replaced by the closing curly bracket "}" and opening curly bracket "{" on purpose.

From f4e7eb7462aac20a2565b41be936ed3d242dd88f Mon Sep 17 00:00:00 2001
From: andrea zuccarini <andrearanma@gmail.com>
Date: Sat, 27 Apr 2019 19:52:19 +0200
Subject: [PATCH 23/55] add encode js file

---
 base64encode_v1-01.js | 96 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 96 insertions(+)
 create mode 100644 base64encode_v1-01.js

diff --git a/base64encode_v1-01.js b/base64encode_v1-01.js
new file mode 100644
index 0000000..5b9add6
--- /dev/null
+++ b/base64encode_v1-01.js
@@ -0,0 +1,96 @@
+//Author: Andrea Zuccarini @2019
+// Version 1.01
+
+//test binary data string: 0b010010010111011111001110010111011101001110001101001011100010011100011101001110011111001110010111010001001010011101100011001010010100010010011100111001000010000000000001001000
+
+//test string as hex: '0x125df39774e34b89c74e7ce5d129d8ca512739080048'
+
+//test string result :'INVENTEDBYSTEVENHATZAKIS@2018'
+
+// legacy notes: #FIX: LEADING ZEROS LOST (i.e.w/ test string 0x064ce8c835f4d374e04e33244beccad0)
+// also, even when no leading zero in string, the leading zeroes of the actual base64 character are discarded,
+// as the encoding appears to happen from right to left, see this test string where leading zeroes of
+// first char 2 are discarded, and last char is N  0xb13ae7e331ce9dfa59799e95ee8dc117
+
+function base64en(address_hex) {  // important never to rename base64en to "base64" which can corrupt the Python installation.
+    // (renamed alphabet to base64library below) alphabet = string.digits+string.ascii_uppercase+string.punctuation
+    base64library=["0",
+    "1",
+    "2",
+    "3",
+    "4",
+    "5",
+    "6",
+    "7",
+    "8",
+    "9",
+    "A",
+    "B",
+    "C",
+    "D",
+    "E",
+    "F",
+    "G",
+    "H",
+    "I",
+    "J",
+    "K",
+    "L",
+    "M",
+    "N",
+    "O",
+    "P",
+    "Q",
+    "R",
+    "S",
+    "T",
+    "U",
+    "V",
+    "W",
+    "X",
+    "Y",
+    "Z",
+    "!",
+    '"',
+    "#",
+    "$",
+    "%",
+    "&",
+    "'",
+    "(",
+    ")",
+    "*",
+    "+",
+    ",",
+    "-",
+    ".",
+    "{",
+    ":",
+    ";",
+    "<",
+    "=",
+    ">",
+    "?",
+    "@",
+    "[",
+    "}",
+    "]",
+    "^",
+    "_",
+    "`"]
+    b64_string = '';
+    // Convert hex to decimal
+    address_int = parseInt(address_hex,16);
+    // Append digits to the start of string
+    while(address_int > 0) {
+        digit = address_int % 64;
+        digit_char = base64library[digit];
+        b64_string = digit_char + b64_string;
+        address_int = parseInt(address_int/64);
+    }
+    return b64_string;
+}
+//hexer=input('enter hex with pad');
+hexer = '0x125df39774e34';
+console.log(base64en(hexer));
+console.log("The above is this many char's long: ", base64en(hexer).length);

From 4a51031b195cc41524815e298fc4ac6e920c91d4 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sat, 27 Apr 2019 15:19:37 -0400
Subject: [PATCH 24/55] Update README.md

---
 README.md | 27 +++++++++++++++++++--------
 1 file changed, 19 insertions(+), 8 deletions(-)

diff --git a/README.md b/README.md
index 215466a..9439738 100644
--- a/README.md
+++ b/README.md
@@ -169,14 +169,9 @@ In Python version 3.7 using the strings library, the following steps can be take
 - Note, the backslash `\` and forwardslash `/`characters were swapped with opening `{` and closing `}` curly brackets in the following issue: https://github.com/hatgit/hatnotation/issues/3. 
 - The list of valid Hatnotation library characters are thus as follows: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_`
 
-(and the following four remain excluded/reserved ~~```"\/|~"```~~).
+- And the following four remain excluded/reserved ~~```"\/|~"```~~).
 
 
-The following Hex string can be fed to the encoder to print all characters in order except for the first which is "0" (zero) and gets omitted: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
-
-The loss of leading zeroes has been discussed in the following issue and is common across notation systems when converting from padded binary data: https://github.com/hatgit/hatnotation/issues/6
-
-** There can be some formatting issues in Python which affect how data is printed as noted in this committ: https://github.com/hatgit/hatnotation/commit/66727918cef8a5bdfad21051d52b9c1e483c7fbc
 
 ## Requirements
 
@@ -187,7 +182,7 @@ Python 3 or higher
 
 ## Tests: 
 
-> Example Test strings: 
+> Example Test strings (note: these are not ASCII notations): 
 
 - Decode Target: `HELLOWORLD
 
@@ -197,9 +192,25 @@ Python 3 or higher
 
 - Concatenation of both words into one string: `"010001001110010101010101011000100000011000011011010101001101"
 
-- Converted binary string to hex (can be used as starting point to encode to "helloworld": `0x44e55562061b54d`
+- Converted binary string to hex (can be used as starting point to encode to "HELLOWORLD": `0x44e55562061b54d`
+
+The following Hex string can be fed to the encoder to print all characters in their linear order except for the first which is "0" (zero) and gets omitted: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
+
+The easiest of this example can be seen using the Hatnotation library of 64 characters as the input: 
+
+0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_`
 
+`The library in binary format as a continous string: 
 
+000000000001000010000011000100000101000110000111001000001001001010001011001100001101001110001111010000010001010010010011010100010101010110010111011000011001011010011011011100011101011110011111100000100001100010100011100100100101100110100111101000101001101010101011101100101110101111110000110001110010110011110100110101110110110111111000111001111010111011111100111101111110111111
+
+(which in hex is: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf)
+which when encoded back to hatnotation loses the leading zero (or first 6 zeroes of the above binary string) resulting in it missing from the start of the resulting encoded characters: "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.}:;<=>?@[{]^_`"
+
+
+The loss of leading zeroes has been discussed in the following issue and is common across notation systems when converting from padded binary data: https://github.com/hatgit/hatnotation/issues/6
+
+** There can be some formatting issues in Python which affect how data is printed as noted in this committ: https://github.com/hatgit/hatnotation/commit/66727918cef8a5bdfad21051d52b9c1e483c7fbc
 
 ## Resources: 
 

From a4dc2096b8a9d56bf78852eacbab219ce8aeb958 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sat, 27 Apr 2019 15:22:10 -0400
Subject: [PATCH 25/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 9439738..24e0d88 100644
--- a/README.md
+++ b/README.md
@@ -184,7 +184,7 @@ Python 3 or higher
 
 > Example Test strings (note: these are not ASCII notations): 
 
-- Decode Target: `HELLOWORLD
+- Decode Target: `HELLOWORLD`
 
 - Each letter decodes to respective 6-bit group: `"010001","001110","010101","010101","011000"," ", "100000","011000","011011","010101","001101",
 

From b397e9f9c02bd19786d7a6fa4ae020177e4f02dc Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sat, 27 Apr 2019 15:27:35 -0400
Subject: [PATCH 26/55] Update README.md

---
 README.md | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/README.md b/README.md
index 24e0d88..d65fac2 100644
--- a/README.md
+++ b/README.md
@@ -194,21 +194,23 @@ Python 3 or higher
 
 - Converted binary string to hex (can be used as starting point to encode to "HELLOWORLD": `0x44e55562061b54d`
 
-The following Hex string can be fed to the encoder to print all characters in their linear order except for the first which is "0" (zero) and gets omitted: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
+>The following Hex string can be fed to the encoder to print all characters in their linear order except for the first which is "0" (zero) and gets omitted: 
 
-The easiest of this example can be seen using the Hatnotation library of 64 characters as the input: 
+0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
+
+The easiest of this example can be seen using the Hatnotation library of 64 characters as the input to the decoder: 
 
 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_`
 
-`The library in binary format as a continous string: 
+The library in binary format as a continous string: 
 
 000000000001000010000011000100000101000110000111001000001001001010001011001100001101001110001111010000010001010010010011010100010101010110010111011000011001011010011011011100011101011110011111100000100001100010100011100100100101100110100111101000101001101010101011101100101110101111110000110001110010110011110100110101110110110111111000111001111010111011111100111101111110111111
 
-(which in hex is: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf)
-which when encoded back to hatnotation loses the leading zero (or first 6 zeroes of the above binary string) resulting in it missing from the start of the resulting encoded characters: "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.}:;<=>?@[{]^_`"
+The above 384-bit binary string (based on 64*6 bits) in hex is: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
 
+When the above hex string is encoded back to hatnotation it loses the leading zero (or first 6 zeroes of the above binary string) resulting in it missing from the start of the resulting encoded characters: "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.}:;<=>?@[{]^_`"
 
-The loss of leading zeroes has been discussed in the following issue and is common across notation systems when converting from padded binary data: https://github.com/hatgit/hatnotation/issues/6
+The loss of leading zeroes has been discussed in the following issue and is common across other popular notation systems when converting from left-padded binary data: https://github.com/hatgit/hatnotation/issues/6
 
 ** There can be some formatting issues in Python which affect how data is printed as noted in this committ: https://github.com/hatgit/hatnotation/commit/66727918cef8a5bdfad21051d52b9c1e483c7fbc
 

From cc3eb75bcf0cf02dba483c303694c6f59032f8b6 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sat, 27 Apr 2019 15:35:02 -0400
Subject: [PATCH 27/55] Update README.md

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index d65fac2..6cbe302 100644
--- a/README.md
+++ b/README.md
@@ -13,7 +13,7 @@ An encoding/decoding method that allows users to compress their human-readable d
 
 ## Warning: 
 
-This software is still in its experimental phase and should not be relied upon for production.  
+This software is still in its experimental phase (including debugging, redesign and error-checking/testing) and should not be relied upon for production.  
 
 ## Background on Mnemonics (private keys) and Human vs Machine-readable code
 
@@ -53,7 +53,7 @@ In terms of actual pre-image resistance, the initial entropy should be generated
 
 ## Important
 
-The Hatnotation system is *not intended to be an alternative to human-readable mnemonics*, but rather a complement and simply another representation of the machine-readable code, with the benefit of a reduction in the number of characters needed to notate and backup/store the data, using common and special characters from a library of 64 total possible characters (in range of 2^6). 
+The Hatnotation system is *not intended to be an alternative to human-readable mnemonics*, but rather a complement and simply another representation of the machine-readable code, with the benefit of a reduction in the number of characters needed to notate and backup/store the data, using common and special characters from a library of 64 total possible characters (in the zero-indexed range of 2^6-1). 
 
 
 

From 016a6c93b46f3cf96eb5cae4850549f74687ea76 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 11:39:09 -0400
Subject: [PATCH 28/55] Created index.html

Html file for use with the Hatnotation encoder and decoder, and using an example BIP39 mnemonic generator from github.com/hatgit/BIP39-Mnemonic-Tools and edits on this gist: https://gist.github.com/johhonn/fea03765fa46280af7dd3563353d0dac
---
 index.html | 2613 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 2613 insertions(+)
 create mode 100644 index.html

diff --git a/index.html b/index.html
new file mode 100644
index 0000000..03f8b1a
--- /dev/null
+++ b/index.html
@@ -0,0 +1,2613 @@
+<html>
+  <head>
+    <title>BIP39 Mnemonic</title>
+    <meta http-equiv="content-type" content="text/html; charset=utf-8" />
+    <script type="text/javascript">
+    "use strict";var sjcl={cipher:{},hash:{},keyexchange:{},mode:{},misc:{},codec:{},exception:{corrupt:function(a){this.toString=function(){return"CORRUPT: "+this.message};this.message=a},invalid:function(a){this.toString=function(){return"INVALID: "+this.message};this.message=a},bug:function(a){this.toString=function(){return"BUG: "+this.message};this.message=a},notReady:function(a){this.toString=function(){return"NOT READY: "+this.message};this.message=a}}};
+sjcl.cipher.aes=function(a){this.s[0][0][0]||this.O();var b,c,d,e,f=this.s[0][4],g=this.s[1];b=a.length;var h=1;if(4!==b&&6!==b&&8!==b)throw new sjcl.exception.invalid("invalid aes key size");this.b=[d=a.slice(0),e=[]];for(a=b;a<4*b+28;a++){c=d[a-1];if(0===a%b||8===b&&4===a%b)c=f[c>>>24]<<24^f[c>>16&255]<<16^f[c>>8&255]<<8^f[c&255],0===a%b&&(c=c<<8^c>>>24^h<<24,h=h<<1^283*(h>>7));d[a]=d[a-b]^c}for(b=0;a;b++,a--)c=d[b&3?a:a-4],e[b]=4>=a||4>b?c:g[0][f[c>>>24]]^g[1][f[c>>16&255]]^g[2][f[c>>8&255]]^g[3][f[c&
+255]]};
+sjcl.cipher.aes.prototype={encrypt:function(a){return t(this,a,0)},decrypt:function(a){return t(this,a,1)},s:[[[],[],[],[],[]],[[],[],[],[],[]]],O:function(){var a=this.s[0],b=this.s[1],c=a[4],d=b[4],e,f,g,h=[],k=[],l,n,m,p;for(e=0;0x100>e;e++)k[(h[e]=e<<1^283*(e>>7))^e]=e;for(f=g=0;!c[f];f^=l||1,g=k[g]||1)for(m=g^g<<1^g<<2^g<<3^g<<4,m=m>>8^m&255^99,c[f]=m,d[m]=f,n=h[e=h[l=h[f]]],p=0x1010101*n^0x10001*e^0x101*l^0x1010100*f,n=0x101*h[m]^0x1010100*m,e=0;4>e;e++)a[e][f]=n=n<<24^n>>>8,b[e][m]=p=p<<24^p>>>8;for(e=
+0;5>e;e++)a[e]=a[e].slice(0),b[e]=b[e].slice(0)}};
+function t(a,b,c){if(4!==b.length)throw new sjcl.exception.invalid("invalid aes block size");var d=a.b[c],e=b[0]^d[0],f=b[c?3:1]^d[1],g=b[2]^d[2];b=b[c?1:3]^d[3];var h,k,l,n=d.length/4-2,m,p=4,r=[0,0,0,0];h=a.s[c];a=h[0];var q=h[1],v=h[2],w=h[3],x=h[4];for(m=0;m<n;m++)h=a[e>>>24]^q[f>>16&255]^v[g>>8&255]^w[b&255]^d[p],k=a[f>>>24]^q[g>>16&255]^v[b>>8&255]^w[e&255]^d[p+1],l=a[g>>>24]^q[b>>16&255]^v[e>>8&255]^w[f&255]^d[p+2],b=a[b>>>24]^q[e>>16&255]^v[f>>8&255]^w[g&255]^d[p+3],p+=4,e=h,f=k,g=l;for(m=
+0;4>m;m++)r[c?3&-m:m]=x[e>>>24]<<24^x[f>>16&255]<<16^x[g>>8&255]<<8^x[b&255]^d[p++],h=e,e=f,f=g,g=b,b=h;return r}
+sjcl.bitArray={bitSlice:function(a,b,c){a=sjcl.bitArray.$(a.slice(b/32),32-(b&31)).slice(1);return void 0===c?a:sjcl.bitArray.clamp(a,c-b)},extract:function(a,b,c){var d=Math.floor(-b-c&31);return((b+c-1^b)&-32?a[b/32|0]<<32-d^a[b/32+1|0]>>>d:a[b/32|0]>>>d)&(1<<c)-1},concat:function(a,b){if(0===a.length||0===b.length)return a.concat(b);var c=a[a.length-1],d=sjcl.bitArray.getPartial(c);return 32===d?a.concat(b):sjcl.bitArray.$(b,d,c|0,a.slice(0,a.length-1))},bitLength:function(a){var b=a.length;return 0===
+b?0:32*(b-1)+sjcl.bitArray.getPartial(a[b-1])},clamp:function(a,b){if(32*a.length<b)return a;a=a.slice(0,Math.ceil(b/32));var c=a.length;b=b&31;0<c&&b&&(a[c-1]=sjcl.bitArray.partial(b,a[c-1]&2147483648>>b-1,1));return a},partial:function(a,b,c){return 32===a?b:(c?b|0:b<<32-a)+0x10000000000*a},getPartial:function(a){return Math.round(a/0x10000000000)||32},equal:function(a,b){if(sjcl.bitArray.bitLength(a)!==sjcl.bitArray.bitLength(b))return!1;var c=0,d;for(d=0;d<a.length;d++)c|=a[d]^b[d];return 0===
+c},$:function(a,b,c,d){var e;e=0;for(void 0===d&&(d=[]);32<=b;b-=32)d.push(c),c=0;if(0===b)return d.concat(a);for(e=0;e<a.length;e++)d.push(c|a[e]>>>b),c=a[e]<<32-b;e=a.length?a[a.length-1]:0;a=sjcl.bitArray.getPartial(e);d.push(sjcl.bitArray.partial(b+a&31,32<b+a?c:d.pop(),1));return d},i:function(a,b){return[a[0]^b[0],a[1]^b[1],a[2]^b[2],a[3]^b[3]]},byteswapM:function(a){var b,c;for(b=0;b<a.length;++b)c=a[b],a[b]=c>>>24|c>>>8&0xff00|(c&0xff00)<<8|c<<24;return a}};
+sjcl.codec.utf8String={fromBits:function(a){var b="",c=sjcl.bitArray.bitLength(a),d,e;for(d=0;d<c/8;d++)0===(d&3)&&(e=a[d/4]),b+=String.fromCharCode(e>>>8>>>8>>>8),e<<=8;return decodeURIComponent(escape(b))},toBits:function(a){a=unescape(encodeURIComponent(a));var b=[],c,d=0;for(c=0;c<a.length;c++)d=d<<8|a.charCodeAt(c),3===(c&3)&&(b.push(d),d=0);c&3&&b.push(sjcl.bitArray.partial(8*(c&3),d));return b}};
+sjcl.codec.hex={fromBits:function(a){var b="",c;for(c=0;c<a.length;c++)b+=((a[c]|0)+0xf00000000000).toString(16).substr(4);return b.substr(0,sjcl.bitArray.bitLength(a)/4)},toBits:function(a){var b,c=[],d;a=a.replace(/\s|0x/g,"");d=a.length;a=a+"00000000";for(b=0;b<a.length;b+=8)c.push(parseInt(a.substr(b,8),16)^0);return sjcl.bitArray.clamp(c,4*d)}};
+sjcl.codec.base32={B:"ABCDEFGHIJKLMNOPQRSTUVWXYZ234567",X:"0123456789ABCDEFGHIJKLMNOPQRSTUV",BITS:32,BASE:5,REMAINING:27,fromBits:function(a,b,c){var d=sjcl.codec.base32.BASE,e=sjcl.codec.base32.REMAINING,f="",g=0,h=sjcl.codec.base32.B,k=0,l=sjcl.bitArray.bitLength(a);c&&(h=sjcl.codec.base32.X);for(c=0;f.length*d<l;)f+=h.charAt((k^a[c]>>>g)>>>e),g<d?(k=a[c]<<d-g,g+=e,c++):(k<<=d,g-=d);for(;f.length&7&&!b;)f+="=";return f},toBits:function(a,b){a=a.replace(/\s|=/g,"").toUpperCase();var c=sjcl.codec.base32.BITS,
+d=sjcl.codec.base32.BASE,e=sjcl.codec.base32.REMAINING,f=[],g,h=0,k=sjcl.codec.base32.B,l=0,n,m="base32";b&&(k=sjcl.codec.base32.X,m="base32hex");for(g=0;g<a.length;g++){n=k.indexOf(a.charAt(g));if(0>n){if(!b)try{return sjcl.codec.base32hex.toBits(a)}catch(p){}throw new sjcl.exception.invalid("this isn't "+m+"!");}h>e?(h-=e,f.push(l^n>>>h),l=n<<c-h):(h+=d,l^=n<<c-h)}h&56&&f.push(sjcl.bitArray.partial(h&56,l,1));return f}};
+sjcl.codec.base32hex={fromBits:function(a,b){return sjcl.codec.base32.fromBits(a,b,1)},toBits:function(a){return sjcl.codec.base32.toBits(a,1)}};
+sjcl.codec.base64={B:"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/",fromBits:function(a,b,c){var d="",e=0,f=sjcl.codec.base64.B,g=0,h=sjcl.bitArray.bitLength(a);c&&(f=f.substr(0,62)+"-_");for(c=0;6*d.length<h;)d+=f.charAt((g^a[c]>>>e)>>>26),6>e?(g=a[c]<<6-e,e+=26,c++):(g<<=6,e-=6);for(;d.length&3&&!b;)d+="=";return d},toBits:function(a,b){a=a.replace(/\s|=/g,"");var c=[],d,e=0,f=sjcl.codec.base64.B,g=0,h;b&&(f=f.substr(0,62)+"-_");for(d=0;d<a.length;d++){h=f.indexOf(a.charAt(d));
+if(0>h)throw new sjcl.exception.invalid("this isn't base64!");26<e?(e-=26,c.push(g^h>>>e),g=h<<32-e):(e+=6,g^=h<<32-e)}e&56&&c.push(sjcl.bitArray.partial(e&56,g,1));return c}};sjcl.codec.base64url={fromBits:function(a){return sjcl.codec.base64.fromBits(a,1,1)},toBits:function(a){return sjcl.codec.base64.toBits(a,1)}};sjcl.hash.sha256=function(a){this.b[0]||this.O();a?(this.F=a.F.slice(0),this.A=a.A.slice(0),this.l=a.l):this.reset()};sjcl.hash.sha256.hash=function(a){return(new sjcl.hash.sha256).update(a).finalize()};
+sjcl.hash.sha256.prototype={blockSize:512,reset:function(){this.F=this.Y.slice(0);this.A=[];this.l=0;return this},update:function(a){"string"===typeof a&&(a=sjcl.codec.utf8String.toBits(a));var b,c=this.A=sjcl.bitArray.concat(this.A,a);b=this.l;a=this.l=b+sjcl.bitArray.bitLength(a);if(0x1fffffffffffff<a)throw new sjcl.exception.invalid("Cannot hash more than 2^53 - 1 bits");if("undefined"!==typeof Uint32Array){var d=new Uint32Array(c),e=0;for(b=512+b-(512+b&0x1ff);b<=a;b+=512)u(this,d.subarray(16*e,
+16*(e+1))),e+=1;c.splice(0,16*e)}else for(b=512+b-(512+b&0x1ff);b<=a;b+=512)u(this,c.splice(0,16));return this},finalize:function(){var a,b=this.A,c=this.F,b=sjcl.bitArray.concat(b,[sjcl.bitArray.partial(1,1)]);for(a=b.length+2;a&15;a++)b.push(0);b.push(Math.floor(this.l/0x100000000));for(b.push(this.l|0);b.length;)u(this,b.splice(0,16));this.reset();return c},Y:[],b:[],O:function(){function a(a){return 0x100000000*(a-Math.floor(a))|0}for(var b=0,c=2,d,e;64>b;c++){e=!0;for(d=2;d*d<=c;d++)if(0===c%d){e=
+!1;break}e&&(8>b&&(this.Y[b]=a(Math.pow(c,.5))),this.b[b]=a(Math.pow(c,1/3)),b++)}}};
+function u(a,b){var c,d,e,f=a.F,g=a.b,h=f[0],k=f[1],l=f[2],n=f[3],m=f[4],p=f[5],r=f[6],q=f[7];for(c=0;64>c;c++)16>c?d=b[c]:(d=b[c+1&15],e=b[c+14&15],d=b[c&15]=(d>>>7^d>>>18^d>>>3^d<<25^d<<14)+(e>>>17^e>>>19^e>>>10^e<<15^e<<13)+b[c&15]+b[c+9&15]|0),d=d+q+(m>>>6^m>>>11^m>>>25^m<<26^m<<21^m<<7)+(r^m&(p^r))+g[c],q=r,r=p,p=m,m=n+d|0,n=l,l=k,k=h,h=d+(k&l^n&(k^l))+(k>>>2^k>>>13^k>>>22^k<<30^k<<19^k<<10)|0;f[0]=f[0]+h|0;f[1]=f[1]+k|0;f[2]=f[2]+l|0;f[3]=f[3]+n|0;f[4]=f[4]+m|0;f[5]=f[5]+p|0;f[6]=f[6]+r|0;f[7]=
+f[7]+q|0}
+sjcl.mode.ccm={name:"ccm",G:[],listenProgress:function(a){sjcl.mode.ccm.G.push(a)},unListenProgress:function(a){a=sjcl.mode.ccm.G.indexOf(a);-1<a&&sjcl.mode.ccm.G.splice(a,1)},fa:function(a){var b=sjcl.mode.ccm.G.slice(),c;for(c=0;c<b.length;c+=1)b[c](a)},encrypt:function(a,b,c,d,e){var f,g=b.slice(0),h=sjcl.bitArray,k=h.bitLength(c)/8,l=h.bitLength(g)/8;e=e||64;d=d||[];if(7>k)throw new sjcl.exception.invalid("ccm: iv must be at least 7 bytes");for(f=2;4>f&&l>>>8*f;f++);f<15-k&&(f=15-k);c=h.clamp(c,
+8*(15-f));b=sjcl.mode.ccm.V(a,b,c,d,e,f);g=sjcl.mode.ccm.C(a,g,c,b,e,f);return h.concat(g.data,g.tag)},decrypt:function(a,b,c,d,e){e=e||64;d=d||[];var f=sjcl.bitArray,g=f.bitLength(c)/8,h=f.bitLength(b),k=f.clamp(b,h-e),l=f.bitSlice(b,h-e),h=(h-e)/8;if(7>g)throw new sjcl.exception.invalid("ccm: iv must be at least 7 bytes");for(b=2;4>b&&h>>>8*b;b++);b<15-g&&(b=15-g);c=f.clamp(c,8*(15-b));k=sjcl.mode.ccm.C(a,k,c,l,e,b);a=sjcl.mode.ccm.V(a,k.data,c,d,e,b);if(!f.equal(k.tag,a))throw new sjcl.exception.corrupt("ccm: tag doesn't match");
+return k.data},na:function(a,b,c,d,e,f){var g=[],h=sjcl.bitArray,k=h.i;d=[h.partial(8,(b.length?64:0)|d-2<<2|f-1)];d=h.concat(d,c);d[3]|=e;d=a.encrypt(d);if(b.length)for(c=h.bitLength(b)/8,65279>=c?g=[h.partial(16,c)]:0xffffffff>=c&&(g=h.concat([h.partial(16,65534)],[c])),g=h.concat(g,b),b=0;b<g.length;b+=4)d=a.encrypt(k(d,g.slice(b,b+4).concat([0,0,0])));return d},V:function(a,b,c,d,e,f){var g=sjcl.bitArray,h=g.i;e/=8;if(e%2||4>e||16<e)throw new sjcl.exception.invalid("ccm: invalid tag length");
+if(0xffffffff<d.length||0xffffffff<b.length)throw new sjcl.exception.bug("ccm: can't deal with 4GiB or more data");c=sjcl.mode.ccm.na(a,d,c,e,g.bitLength(b)/8,f);for(d=0;d<b.length;d+=4)c=a.encrypt(h(c,b.slice(d,d+4).concat([0,0,0])));return g.clamp(c,8*e)},C:function(a,b,c,d,e,f){var g,h=sjcl.bitArray;g=h.i;var k=b.length,l=h.bitLength(b),n=k/50,m=n;c=h.concat([h.partial(8,f-1)],c).concat([0,0,0]).slice(0,4);d=h.bitSlice(g(d,a.encrypt(c)),0,e);if(!k)return{tag:d,data:[]};for(g=0;g<k;g+=4)g>n&&(sjcl.mode.ccm.fa(g/
+k),n+=m),c[3]++,e=a.encrypt(c),b[g]^=e[0],b[g+1]^=e[1],b[g+2]^=e[2],b[g+3]^=e[3];return{tag:d,data:h.clamp(b,l)}}};
+sjcl.mode.ocb2={name:"ocb2",encrypt:function(a,b,c,d,e,f){if(128!==sjcl.bitArray.bitLength(c))throw new sjcl.exception.invalid("ocb iv must be 128 bits");var g,h=sjcl.mode.ocb2.S,k=sjcl.bitArray,l=k.i,n=[0,0,0,0];c=h(a.encrypt(c));var m,p=[];d=d||[];e=e||64;for(g=0;g+4<b.length;g+=4)m=b.slice(g,g+4),n=l(n,m),p=p.concat(l(c,a.encrypt(l(c,m)))),c=h(c);m=b.slice(g);b=k.bitLength(m);g=a.encrypt(l(c,[0,0,0,b]));m=k.clamp(l(m.concat([0,0,0]),g),b);n=l(n,l(m.concat([0,0,0]),g));n=a.encrypt(l(n,l(c,h(c))));
+d.length&&(n=l(n,f?d:sjcl.mode.ocb2.pmac(a,d)));return p.concat(k.concat(m,k.clamp(n,e)))},decrypt:function(a,b,c,d,e,f){if(128!==sjcl.bitArray.bitLength(c))throw new sjcl.exception.invalid("ocb iv must be 128 bits");e=e||64;var g=sjcl.mode.ocb2.S,h=sjcl.bitArray,k=h.i,l=[0,0,0,0],n=g(a.encrypt(c)),m,p,r=sjcl.bitArray.bitLength(b)-e,q=[];d=d||[];for(c=0;c+4<r/32;c+=4)m=k(n,a.decrypt(k(n,b.slice(c,c+4)))),l=k(l,m),q=q.concat(m),n=g(n);p=r-32*c;m=a.encrypt(k(n,[0,0,0,p]));m=k(m,h.clamp(b.slice(c),p).concat([0,
+0,0]));l=k(l,m);l=a.encrypt(k(l,k(n,g(n))));d.length&&(l=k(l,f?d:sjcl.mode.ocb2.pmac(a,d)));if(!h.equal(h.clamp(l,e),h.bitSlice(b,r)))throw new sjcl.exception.corrupt("ocb: tag doesn't match");return q.concat(h.clamp(m,p))},pmac:function(a,b){var c,d=sjcl.mode.ocb2.S,e=sjcl.bitArray,f=e.i,g=[0,0,0,0],h=a.encrypt([0,0,0,0]),h=f(h,d(d(h)));for(c=0;c+4<b.length;c+=4)h=d(h),g=f(g,a.encrypt(f(h,b.slice(c,c+4))));c=b.slice(c);128>e.bitLength(c)&&(h=f(h,d(h)),c=e.concat(c,[-2147483648,0,0,0]));g=f(g,c);
+return a.encrypt(f(d(f(h,d(h))),g))},S:function(a){return[a[0]<<1^a[1]>>>31,a[1]<<1^a[2]>>>31,a[2]<<1^a[3]>>>31,a[3]<<1^135*(a[0]>>>31)]}};
+sjcl.mode.gcm={name:"gcm",encrypt:function(a,b,c,d,e){var f=b.slice(0);b=sjcl.bitArray;d=d||[];a=sjcl.mode.gcm.C(!0,a,f,d,c,e||128);return b.concat(a.data,a.tag)},decrypt:function(a,b,c,d,e){var f=b.slice(0),g=sjcl.bitArray,h=g.bitLength(f);e=e||128;d=d||[];e<=h?(b=g.bitSlice(f,h-e),f=g.bitSlice(f,0,h-e)):(b=f,f=[]);a=sjcl.mode.gcm.C(!1,a,f,d,c,e);if(!g.equal(a.tag,b))throw new sjcl.exception.corrupt("gcm: tag doesn't match");return a.data},ka:function(a,b){var c,d,e,f,g,h=sjcl.bitArray.i;e=[0,0,
+0,0];f=b.slice(0);for(c=0;128>c;c++){(d=0!==(a[Math.floor(c/32)]&1<<31-c%32))&&(e=h(e,f));g=0!==(f[3]&1);for(d=3;0<d;d--)f[d]=f[d]>>>1|(f[d-1]&1)<<31;f[0]>>>=1;g&&(f[0]^=-0x1f000000)}return e},j:function(a,b,c){var d,e=c.length;b=b.slice(0);for(d=0;d<e;d+=4)b[0]^=0xffffffff&c[d],b[1]^=0xffffffff&c[d+1],b[2]^=0xffffffff&c[d+2],b[3]^=0xffffffff&c[d+3],b=sjcl.mode.gcm.ka(b,a);return b},C:function(a,b,c,d,e,f){var g,h,k,l,n,m,p,r,q=sjcl.bitArray;m=c.length;p=q.bitLength(c);r=q.bitLength(d);h=q.bitLength(e);
+g=b.encrypt([0,0,0,0]);96===h?(e=e.slice(0),e=q.concat(e,[1])):(e=sjcl.mode.gcm.j(g,[0,0,0,0],e),e=sjcl.mode.gcm.j(g,e,[0,0,Math.floor(h/0x100000000),h&0xffffffff]));h=sjcl.mode.gcm.j(g,[0,0,0,0],d);n=e.slice(0);d=h.slice(0);a||(d=sjcl.mode.gcm.j(g,h,c));for(l=0;l<m;l+=4)n[3]++,k=b.encrypt(n),c[l]^=k[0],c[l+1]^=k[1],c[l+2]^=k[2],c[l+3]^=k[3];c=q.clamp(c,p);a&&(d=sjcl.mode.gcm.j(g,h,c));a=[Math.floor(r/0x100000000),r&0xffffffff,Math.floor(p/0x100000000),p&0xffffffff];d=sjcl.mode.gcm.j(g,d,a);k=b.encrypt(e);
+d[0]^=k[0];d[1]^=k[1];d[2]^=k[2];d[3]^=k[3];return{tag:q.bitSlice(d,0,f),data:c}}};sjcl.misc.hmac=function(a,b){this.W=b=b||sjcl.hash.sha256;var c=[[],[]],d,e=b.prototype.blockSize/32;this.w=[new b,new b];a.length>e&&(a=b.hash(a));for(d=0;d<e;d++)c[0][d]=a[d]^909522486,c[1][d]=a[d]^1549556828;this.w[0].update(c[0]);this.w[1].update(c[1]);this.R=new b(this.w[0])};
+sjcl.misc.hmac.prototype.encrypt=sjcl.misc.hmac.prototype.mac=function(a){if(this.aa)throw new sjcl.exception.invalid("encrypt on already updated hmac called!");this.update(a);return this.digest(a)};sjcl.misc.hmac.prototype.reset=function(){this.R=new this.W(this.w[0]);this.aa=!1};sjcl.misc.hmac.prototype.update=function(a){this.aa=!0;this.R.update(a)};sjcl.misc.hmac.prototype.digest=function(){var a=this.R.finalize(),a=(new this.W(this.w[1])).update(a).finalize();this.reset();return a};
+sjcl.misc.pbkdf2=function(a,b,c,d,e){c=c||1E4;if(0>d||0>c)throw new sjcl.exception.invalid("invalid params to pbkdf2");"string"===typeof a&&(a=sjcl.codec.utf8String.toBits(a));"string"===typeof b&&(b=sjcl.codec.utf8String.toBits(b));e=e||sjcl.misc.hmac;a=new e(a);var f,g,h,k,l=[],n=sjcl.bitArray;for(k=1;32*l.length<(d||1);k++){e=f=a.encrypt(n.concat(b,[k]));for(g=1;g<c;g++)for(f=a.encrypt(f),h=0;h<f.length;h++)e[h]^=f[h];l=l.concat(e)}d&&(l=n.clamp(l,d));return l};
+sjcl.prng=function(a){this.c=[new sjcl.hash.sha256];this.m=[0];this.P=0;this.H={};this.N=0;this.U={};this.Z=this.f=this.o=this.ha=0;this.b=[0,0,0,0,0,0,0,0];this.h=[0,0,0,0];this.L=void 0;this.M=a;this.D=!1;this.K={progress:{},seeded:{}};this.u=this.ga=0;this.I=1;this.J=2;this.ca=0x10000;this.T=[0,48,64,96,128,192,0x100,384,512,768,1024];this.da=3E4;this.ba=80};
+sjcl.prng.prototype={randomWords:function(a,b){var c=[],d;d=this.isReady(b);var e;if(d===this.u)throw new sjcl.exception.notReady("generator isn't seeded");if(d&this.J){d=!(d&this.I);e=[];var f=0,g;this.Z=e[0]=(new Date).valueOf()+this.da;for(g=0;16>g;g++)e.push(0x100000000*Math.random()|0);for(g=0;g<this.c.length&&(e=e.concat(this.c[g].finalize()),f+=this.m[g],this.m[g]=0,d||!(this.P&1<<g));g++);this.P>=1<<this.c.length&&(this.c.push(new sjcl.hash.sha256),this.m.push(0));this.f-=f;f>this.o&&(this.o=
+f);this.P++;this.b=sjcl.hash.sha256.hash(this.b.concat(e));this.L=new sjcl.cipher.aes(this.b);for(d=0;4>d&&(this.h[d]=this.h[d]+1|0,!this.h[d]);d++);}for(d=0;d<a;d+=4)0===(d+1)%this.ca&&y(this),e=z(this),c.push(e[0],e[1],e[2],e[3]);y(this);return c.slice(0,a)},setDefaultParanoia:function(a,b){if(0===a&&"Setting paranoia=0 will ruin your security; use it only for testing"!==b)throw new sjcl.exception.invalid("Setting paranoia=0 will ruin your security; use it only for testing");this.M=a},addEntropy:function(a,
+b,c){c=c||"user";var d,e,f=(new Date).valueOf(),g=this.H[c],h=this.isReady(),k=0;d=this.U[c];void 0===d&&(d=this.U[c]=this.ha++);void 0===g&&(g=this.H[c]=0);this.H[c]=(this.H[c]+1)%this.c.length;switch(typeof a){case "number":void 0===b&&(b=1);this.c[g].update([d,this.N++,1,b,f,1,a|0]);break;case "object":c=Object.prototype.toString.call(a);if("[object Uint32Array]"===c){e=[];for(c=0;c<a.length;c++)e.push(a[c]);a=e}else for("[object Array]"!==c&&(k=1),c=0;c<a.length&&!k;c++)"number"!==typeof a[c]&&
+(k=1);if(!k){if(void 0===b)for(c=b=0;c<a.length;c++)for(e=a[c];0<e;)b++,e=e>>>1;this.c[g].update([d,this.N++,2,b,f,a.length].concat(a))}break;case "string":void 0===b&&(b=a.length);this.c[g].update([d,this.N++,3,b,f,a.length]);this.c[g].update(a);break;default:k=1}if(k)throw new sjcl.exception.bug("random: addEntropy only supports number, array of numbers or string");this.m[g]+=b;this.f+=b;h===this.u&&(this.isReady()!==this.u&&A("seeded",Math.max(this.o,this.f)),A("progress",this.getProgress()))},
+isReady:function(a){a=this.T[void 0!==a?a:this.M];return this.o&&this.o>=a?this.m[0]>this.ba&&(new Date).valueOf()>this.Z?this.J|this.I:this.I:this.f>=a?this.J|this.u:this.u},getProgress:function(a){a=this.T[a?a:this.M];return this.o>=a?1:this.f>a?1:this.f/a},startCollectors:function(){if(!this.D){this.a={loadTimeCollector:B(this,this.ma),mouseCollector:B(this,this.oa),keyboardCollector:B(this,this.la),accelerometerCollector:B(this,this.ea),touchCollector:B(this,this.qa)};if(window.addEventListener)window.addEventListener("load",
+this.a.loadTimeCollector,!1),window.addEventListener("mousemove",this.a.mouseCollector,!1),window.addEventListener("keypress",this.a.keyboardCollector,!1),window.addEventListener("devicemotion",this.a.accelerometerCollector,!1),window.addEventListener("touchmove",this.a.touchCollector,!1);else if(document.attachEvent)document.attachEvent("onload",this.a.loadTimeCollector),document.attachEvent("onmousemove",this.a.mouseCollector),document.attachEvent("keypress",this.a.keyboardCollector);else throw new sjcl.exception.bug("can't attach event");
+this.D=!0}},stopCollectors:function(){this.D&&(window.removeEventListener?(window.removeEventListener("load",this.a.loadTimeCollector,!1),window.removeEventListener("mousemove",this.a.mouseCollector,!1),window.removeEventListener("keypress",this.a.keyboardCollector,!1),window.removeEventListener("devicemotion",this.a.accelerometerCollector,!1),window.removeEventListener("touchmove",this.a.touchCollector,!1)):document.detachEvent&&(document.detachEvent("onload",this.a.loadTimeCollector),document.detachEvent("onmousemove",
+this.a.mouseCollector),document.detachEvent("keypress",this.a.keyboardCollector)),this.D=!1)},addEventListener:function(a,b){this.K[a][this.ga++]=b},removeEventListener:function(a,b){var c,d,e=this.K[a],f=[];for(d in e)e.hasOwnProperty(d)&&e[d]===b&&f.push(d);for(c=0;c<f.length;c++)d=f[c],delete e[d]},la:function(){C(this,1)},oa:function(a){var b,c;try{b=a.x||a.clientX||a.offsetX||0,c=a.y||a.clientY||a.offsetY||0}catch(d){c=b=0}0!=b&&0!=c&&this.addEntropy([b,c],2,"mouse");C(this,0)},qa:function(a){a=
+a.touches[0]||a.changedTouches[0];this.addEntropy([a.pageX||a.clientX,a.pageY||a.clientY],1,"touch");C(this,0)},ma:function(){C(this,2)},ea:function(a){a=a.accelerationIncludingGravity.x||a.accelerationIncludingGravity.y||a.accelerationIncludingGravity.z;if(window.orientation){var b=window.orientation;"number"===typeof b&&this.addEntropy(b,1,"accelerometer")}a&&this.addEntropy(a,2,"accelerometer");C(this,0)}};
+function A(a,b){var c,d=sjcl.random.K[a],e=[];for(c in d)d.hasOwnProperty(c)&&e.push(d[c]);for(c=0;c<e.length;c++)e[c](b)}function C(a,b){"undefined"!==typeof window&&window.performance&&"function"===typeof window.performance.now?a.addEntropy(window.performance.now(),b,"loadtime"):a.addEntropy((new Date).valueOf(),b,"loadtime")}function y(a){a.b=z(a).concat(z(a));a.L=new sjcl.cipher.aes(a.b)}function z(a){for(var b=0;4>b&&(a.h[b]=a.h[b]+1|0,!a.h[b]);b++);return a.L.encrypt(a.h)}
+function B(a,b){return function(){b.apply(a,arguments)}}sjcl.random=new sjcl.prng(6);
+a:try{var D,E,F,G;if(G="undefined"!==typeof module&&module.exports){var H;try{H=require("crypto")}catch(a){H=null}G=E=H}if(G&&E.randomBytes)D=E.randomBytes(128),D=new Uint32Array((new Uint8Array(D)).buffer),sjcl.random.addEntropy(D,1024,"crypto['randomBytes']");else if("undefined"!==typeof window&&"undefined"!==typeof Uint32Array){F=new Uint32Array(32);if(window.crypto&&window.crypto.getRandomValues)window.crypto.getRandomValues(F);else if(window.msCrypto&&window.msCrypto.getRandomValues)window.msCrypto.getRandomValues(F);
+else break a;sjcl.random.addEntropy(F,1024,"crypto['getRandomValues']")}}catch(a){"undefined"!==typeof window&&window.console&&(console.log("There was an error collecting entropy from the browser:"),console.log(a))}
+sjcl.json={defaults:{v:1,iter:1E4,ks:128,ts:64,mode:"ccm",adata:"",cipher:"aes"},ja:function(a,b,c,d){c=c||{};d=d||{};var e=sjcl.json,f=e.g({iv:sjcl.random.randomWords(4,0)},e.defaults),g;e.g(f,c);c=f.adata;"string"===typeof f.salt&&(f.salt=sjcl.codec.base64.toBits(f.salt));"string"===typeof f.iv&&(f.iv=sjcl.codec.base64.toBits(f.iv));if(!sjcl.mode[f.mode]||!sjcl.cipher[f.cipher]||"string"===typeof a&&100>=f.iter||64!==f.ts&&96!==f.ts&&128!==f.ts||128!==f.ks&&192!==f.ks&&0x100!==f.ks||2>f.iv.length||
+4<f.iv.length)throw new sjcl.exception.invalid("json encrypt: invalid parameters");"string"===typeof a?(g=sjcl.misc.cachedPbkdf2(a,f),a=g.key.slice(0,f.ks/32),f.salt=g.salt):sjcl.ecc&&a instanceof sjcl.ecc.elGamal.publicKey&&(g=a.kem(),f.kemtag=g.tag,a=g.key.slice(0,f.ks/32));"string"===typeof b&&(b=sjcl.codec.utf8String.toBits(b));"string"===typeof c&&(f.adata=c=sjcl.codec.utf8String.toBits(c));g=new sjcl.cipher[f.cipher](a);e.g(d,f);d.key=a;f.ct="ccm"===f.mode&&sjcl.arrayBuffer&&sjcl.arrayBuffer.ccm&&
+b instanceof ArrayBuffer?sjcl.arrayBuffer.ccm.encrypt(g,b,f.iv,c,f.ts):sjcl.mode[f.mode].encrypt(g,b,f.iv,c,f.ts);return f},encrypt:function(a,b,c,d){var e=sjcl.json,f=e.ja.apply(e,arguments);return e.encode(f)},ia:function(a,b,c,d){c=c||{};d=d||{};var e=sjcl.json;b=e.g(e.g(e.g({},e.defaults),b),c,!0);var f,g;f=b.adata;"string"===typeof b.salt&&(b.salt=sjcl.codec.base64.toBits(b.salt));"string"===typeof b.iv&&(b.iv=sjcl.codec.base64.toBits(b.iv));if(!sjcl.mode[b.mode]||!sjcl.cipher[b.cipher]||"string"===
+typeof a&&100>=b.iter||64!==b.ts&&96!==b.ts&&128!==b.ts||128!==b.ks&&192!==b.ks&&0x100!==b.ks||!b.iv||2>b.iv.length||4<b.iv.length)throw new sjcl.exception.invalid("json decrypt: invalid parameters");"string"===typeof a?(g=sjcl.misc.cachedPbkdf2(a,b),a=g.key.slice(0,b.ks/32),b.salt=g.salt):sjcl.ecc&&a instanceof sjcl.ecc.elGamal.secretKey&&(a=a.unkem(sjcl.codec.base64.toBits(b.kemtag)).slice(0,b.ks/32));"string"===typeof f&&(f=sjcl.codec.utf8String.toBits(f));g=new sjcl.cipher[b.cipher](a);f="ccm"===
+b.mode&&sjcl.arrayBuffer&&sjcl.arrayBuffer.ccm&&b.ct instanceof ArrayBuffer?sjcl.arrayBuffer.ccm.decrypt(g,b.ct,b.iv,b.tag,f,b.ts):sjcl.mode[b.mode].decrypt(g,b.ct,b.iv,f,b.ts);e.g(d,b);d.key=a;return 1===c.raw?f:sjcl.codec.utf8String.fromBits(f)},decrypt:function(a,b,c,d){var e=sjcl.json;return e.ia(a,e.decode(b),c,d)},encode:function(a){var b,c="{",d="";for(b in a)if(a.hasOwnProperty(b)){if(!b.match(/^[a-z0-9]+$/i))throw new sjcl.exception.invalid("json encode: invalid property name");c+=d+'"'+
+b+'":';d=",";switch(typeof a[b]){case "number":case "boolean":c+=a[b];break;case "string":c+='"'+escape(a[b])+'"';break;case "object":c+='"'+sjcl.codec.base64.fromBits(a[b],0)+'"';break;default:throw new sjcl.exception.bug("json encode: unsupported type");}}return c+"}"},decode:function(a){a=a.replace(/\s/g,"");if(!a.match(/^\{.*\}$/))throw new sjcl.exception.invalid("json decode: this isn't json!");a=a.replace(/^\{|\}$/g,"").split(/,/);var b={},c,d;for(c=0;c<a.length;c++){if(!(d=a[c].match(/^\s*(?:(["']?)([a-z][a-z0-9]*)\1)\s*:\s*(?:(-?\d+)|"([a-z0-9+\/%*_.@=\-]*)"|(true|false))$/i)))throw new sjcl.exception.invalid("json decode: this isn't json!");
+null!=d[3]?b[d[2]]=parseInt(d[3],10):null!=d[4]?b[d[2]]=d[2].match(/^(ct|adata|salt|iv)$/)?sjcl.codec.base64.toBits(d[4]):unescape(d[4]):null!=d[5]&&(b[d[2]]="true"===d[5])}return b},g:function(a,b,c){void 0===a&&(a={});if(void 0===b)return a;for(var d in b)if(b.hasOwnProperty(d)){if(c&&void 0!==a[d]&&a[d]!==b[d])throw new sjcl.exception.invalid("required parameter overridden");a[d]=b[d]}return a},sa:function(a,b){var c={},d;for(d in a)a.hasOwnProperty(d)&&a[d]!==b[d]&&(c[d]=a[d]);return c},ra:function(a,
+b){var c={},d;for(d=0;d<b.length;d++)void 0!==a[b[d]]&&(c[b[d]]=a[b[d]]);return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.pa={};sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.pa,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=void 0===b.salt?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};
+"undefined"!==typeof module&&module.exports&&(module.exports=sjcl);"function"===typeof define&&define([],function(){return sjcl});
+    </script>
+    <script src='./bignumber.js'></script>
+    <script type="text/javascript">
+    // bip39 Valid Mnemonic Generator Javascript App
+    /*
+    Author: Steven Hatzakis @ 2018
+
+    Version 2.1 beta
+
+    Description: A simplified javascript program for generating
+    valid bip39 mnemonics, using an initial random entropy via the
+    secrets module in Javascript for cryptographically secure entropy,
+    then revealing the entropy in its various formats including hex,
+    and as a bytearray before hashing to obtain the leading required
+    number of bits from the hash digest in order to compute the
+    checksum and complete the final word group.
+
+    Formula: Initial entropy in bits /32 = checksum length in bits
+    initial entropy mod 11 = remaining bits + checksum = last word
+    Initial entropy + checksum = total bits /11 = total words.
+
+    Example usage: 128 bits entropy, will require a 4 bit checksum,
+    for a total of 132 bits.
+
+    Notes: while this code could be re-written to further condense/clean it,
+    my goal was initially just to get it to work. For example, starting with the
+    secret.randbits() function, I noticed often the value returned was less
+    than the range specified even using rangebelow(), so I went a few bits higher
+    in length to help assure that I got at least 129 bits (or 130) and then from
+    there slice at least 128 bits to obtain the desired starting amount of entorpy
+    neeeded.
+
+
+    */
+
+    "use strict"
+
+    function generateBIP39() {
+        output = ''
+        const wordCount = document.getElementById('wordLength').value;
+        addElementToOutput('Number of mnemonic words:',wordCount)
+        var entropy = document.getElementById('entropy').value;
+        const checksumBitCount = Math.floor(wordCount/3)
+	   
+        const totalBitCount = wordCount * 11
+        const generatedBitCount = totalBitCount - checksumBitCount
+        const generatedCharCount = Math.floor(generatedBitCount/4)
+        entropy = checkEntropy(entropy, generatedBitCount, generatedCharCount)
+        if(entropy == null) {
+          alert('check the correctness of entropy inserted and generate again.')
+          return
+        }
+        const entropyWithChecksum = getHash(entropy, generatedCharCount, checksumBitCount)
+        const words = pickWords(entropyWithChecksum)
+        output += 'mnemonic is valid.<br />'
+        output = addWordsToOutput(words) + output
+        document.getElementById('output').innerHTML = output;
+    }
+
+    function generateBIP39Palindromic() {
+        var palindromic = false
+        var firstTimeEntropy = true
+        
+        
+        var countMnemonic = 0
+        const wordCountPal = document.getElementById('wordLengthPal').value;
+        var entropyPal = document.getElementById('entropyPal').value;
+        const checksumBitCount = Math.floor(wordCountPal/3)
+        const totalBitCount = wordCountPal * 11
+        const generatedBitCount = totalBitCount - checksumBitCount
+        const generatedCharCount = Math.floor(generatedBitCount/4)
+        entropyPal = checkEntropy(entropyPal, generatedBitCount, generatedCharCount)
+        if(entropyPal == null) {
+            alert('check the correctness of entropy inserted and generate again.')
+            return
+        }
+        while(!palindromic) {
+            outputPal = ''
+            addElementToOutput('Number of mnemonic words:',wordCountPal,'palindromic')
+            if(firstTimeEntropy) {
+                firstTimeEntropy = false
+            } else {
+                if(countMnemonic==1) {
+                  alert('The first attempt to find a palindromic mnemonic has failed, the application will now continue generating random entropy until it finds a valid palindromic mnemonic.')
+                }
+                entropyPal = generateEntropy(generatedBitCount)
+            }
+            countMnemonic += 1
+            const entropyWithChecksum = getHash(entropyPal, generatedCharCount, checksumBitCount,'palindromic')
+            const words = pickWords(entropyWithChecksum)
+            const checksumToCompare = entropyWithChecksum.slice(11-checksumBitCount,11)
+            addElementToOutput('Last ' + checksumBitCount + ' bits of the first word to compare with checksum of mnemonic reverse order (hex to bits)', checksumToCompare, 'palindromic')
+            const entropyReverseWords = reverseOrder(entropyWithChecksum)
+            const entropyReverseWordsNoLastBits = entropyReverseWords.slice(0,-checksumBitCount)
+            addElementToOutput('Words reverse order = total bits:', entropyReverseWords, 'palindromic')
+            addElementToOutput('Words reverse order without last ' + checksumBitCount + ' bits = total bits:', entropyReverseWordsNoLastBits, 'palindromic')
+            const entropyReverseByteArray = binaryStringToByteArray(entropyReverseWordsNoLastBits)
+            const entropyReverseWithChecksum = getHash(entropyReverseByteArray, generatedCharCount, checksumBitCount, 'palindromic')
+            const checksumReverse = entropyReverseWithChecksum.slice(-checksumBitCount)
+            addElementToOutput('Checksum reverse order (hex to bits)', checksumReverse)
+            if(checksumToCompare==checksumReverse) {
+                outputPal += checksumToCompare + " is equal to " + checksumReverse + ". It is a palindromic mnemonic.</br >"
+                outputPal += "It has been found after " + countMnemonic + " mnemonics attempt.</br >"
+                palindromic = true
+                outputPal = addWordsToOutput(words) + outputPal
+                document.getElementById("outputPal").innerHTML = outputPal;
+            }
+        }
+
+    }
+
+    function checkEntropy(entropy, generatedBitCount, generatedCharCount) {
+        if(entropy.length == 0) {
+            entropy = generateEntropy(generatedBitCount)
+        } else if(entropy.length == generatedCharCount + 2 && entropy.slice(0,2) == '0x') {
+            // skip 0x char in entropy
+            var entropyBinaryTemp = hexStringToBinaryString(entropy.slice(2))
+            entropy = binaryStringToByteArray(entropyBinaryTemp)
+            if(entropyBinaryTemp.includes('NaN')) {
+                return null
+            }
+        } else {
+            return null
+        }
+        return entropy
+    }
+
+    function addWordsToOutput(words) {
+      var mnemonicOutput = ''
+      mnemonicOutput += "Generated mnemonic words:<br />"
+      mnemonicOutput += "<textarea rows='3' cols='100'>"+words.join(' ')+"<"+"/textarea>"
+      mnemonicOutput += "<br /><br />"
+      return mnemonicOutput
+
+    }
+
+    function addElementToOutput(details,value,mode='classic') {
+        if(mode=='classic') {
+            output += details + "<br />"
+            output += value
+            output += "<br /><br />"
+        } else if(mode=='palindromic') {
+            outputPal += details + "<br />"
+            outputPal += value
+            outputPal += "<br /><br />"
+        }
+    }
+
+    function reverseOrder(entropyHash) {
+        var reverseOrder = [];
+        const blen = entropyHash.length / 11;
+        for(var i=0; i<blen; i++) {
+            var idx = entropyHash.substring(i * 11, (i + 1) * 11);
+            reverseOrder.unshift(idx)
+        }
+        return reverseOrder.join('')
+    }
+
+    // It generates entropy as bytearray
+    function generateEntropy(generatedBitCount) {
+        const buffer = new Uint8Array(generatedBitCount/8)
+        const entropy = crypto.getRandomValues(buffer)
+        if(entropy.length % 4 > 0) {
+            throw 'Data length in bits should be divisible by 32, but it is not (' + entropy.length + ' bytes = ' + entropy.length*8 + ' bits).'
+        }
+        return entropy
+    }
+
+    function byteArrayToWordArray(data) {
+        var a = [];
+        for(var i=0; i<data.length/4; i++) {
+            var v = 0;
+            v += data[i*4 + 0] << 8 * 3;
+            v += data[i*4 + 1] << 8 * 2;
+            v += data[i*4 + 2] << 8 * 1;
+            v += data[i*4 + 3] << 8 * 0;
+            a.push(v);
+        }
+        return a;
+    }
+
+    function byteArrayToBinaryString(data) {
+        var bin = "";
+        for(var i=0; i<data.length; i++) {
+            bin += zfill(data[i].toString(2), 8);
+        }
+        return bin;
+    }
+
+    function binaryStringToByteArray(data) {
+        var byteArray = []
+        for(var i=0; i<data.length; i=i+8) {
+          byteArray.push(parseInt(data.slice(i,i+8),2))
+        }
+        return byteArray
+    }
+    function HexstringToByteArray(data) {
+        var byteArray = []
+        
+        for(var i=0; i<data.length; i=i+2) {
+            console.log(data.slice(i,i+2))  
+          byteArray.push(parseInt(data.slice(i,i+2),16))
+        }
+        return byteArray
+    }
+
+    // Pad a numeric string on the left with zero digits until the given width
+    // is reached.
+    // Note this differs to the python implementation because it does not
+    // handle numbers starting with a sign.
+    function zfill(source, length) {
+        var source = source.toString();
+        while (source.length < length) {
+            source = '0' + source;
+        }
+        return source;
+    }
+
+    function hexStringToBinaryString(hexString) {
+        var binaryString = "";
+        for(var i=0; i<hexString.length; i++) {
+            binaryString += zfill(parseInt(hexString[i], 16).toString(2),4)
+        }
+        return binaryString;
+    }
+
+    function getHash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic') {
+        console.log(generatedCharCount)
+        console.log(entropyBytearray)
+        console.log(checksumBitCount)
+        const entropyBinary = byteArrayToBinaryString(entropyBytearray)
+        const data = byteArrayToWordArray(entropyBytearray)
+        const hexData = '0x' + sjcl.codec.hex.fromBits(data)
+        const hexDataNoPadding = hexData.slice(2)
+        // sha256
+        const hash = sjcl.hash.sha256.hash(data)
+        const hashHex = sjcl.codec.hex.fromBits(hash)
+        //console.log(hexData)
+        //console.log(hashHex)
+       // console.log(entropyBinary)
+        console.log(hexStringToBinaryString(hashHex))
+        const c = zfill(hexStringToBinaryString(hashHex), 256)
+        const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+        const checksumCharCount = Math.floor(checksumBitCount/4)
+        const bit = hashHex.slice(0,checksumCharCount)
+        // final entropy + checksum bits
+        const b = entropyBinary + checksum;
+        const hatNotation= base64en(hexData)
+        addElementToOutput('Initial entropy:', entropyBinary, mode)
+        addElementToOutput('Length of initial entropy:', entropyBinary.length, mode)
+        addElementToOutput('Initial entropy as hex:', hexData, mode)
+        addElementToOutput('Length of entropy as hex:', hexData.length, mode)
+        addElementToOutput('Entropy as Base64:', hatNotation, mode)
+        addElementToOutput('gcc:', generatedCharCount, mode)
+        addElementToOutput('Entropy length as hex without 0x pad:', hexDataNoPadding.length, mode)
+        addElementToOutput('Initial entropy as hex without pad:', hexDataNoPadding, mode)
+        addElementToOutput('Entropy as bytes:', entropyBytearray.join(' '), mode)
+        addElementToOutput('Length of initial entropy as bytearray:', entropyBytearray.length, mode)
+        addElementToOutput('SHA-256 hash digest of entropy bytes', hashHex, mode)
+        addElementToOutput('Partial fragment of initial "byte" of hash', bit, mode)
+        addElementToOutput('First n bits of hash to convert to hex', bit.slice(0,checksumCharCount), mode)
+        addElementToOutput('Checksum (hex to bits)', checksum, mode)
+        addElementToOutput('Initial entropy + checksum = total bits:', b, mode)
+        addElementToOutput('Length of total bits:', b.length, mode)
+        addElementToOutput('Optional backup hex:', hexData, mode)
+        addElementToOutput('Optional backup hex with checksum:', hexData + parseInt(checksum, 2).toString(16), mode)
+        addElementToOutput('Hash digest of initial entropy bytes:', hashHex, mode)
+        return b
+    }
+    function getDecodedhash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic'){
+        console.log(generatedCharCount)
+        console.log(entropyBytearray)
+        console.log(checksumBitCount)
+        const entropyBinary = byteArrayToBinaryString(entropyBytearray)
+        const data = byteArrayToWordArray(entropyBytearray)
+        const hexData = '0x' + sjcl.codec.hex.fromBits(data)
+        const hexDataNoPadding = hexData.slice(2)
+        // sha256
+        const hash = sjcl.hash.sha256.hash(data)
+        const hashHex = sjcl.codec.hex.fromBits(hash)
+        //console.log(hexData)
+        //console.log(hashHex)
+       // console.log(entropyBinary)
+        console.log(hexStringToBinaryString(hashHex))
+        const c = zfill(hexStringToBinaryString(hashHex), 256)
+        const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+        const checksumCharCount = Math.floor(checksumBitCount/4)
+        const bit = hashHex.slice(0,checksumCharCount)
+        // final entropy + checksum bits
+        const b = entropyBinary + checksum;
+        
+      
+        return b
+    }
+    function Decrypt(){
+        var entropy64 = document.getElementById('base64entropy').value;
+        console.log(entropy64)
+        var hex=decodeAsHex(entropy64)
+        hex=hex.slice(1)
+        var hex2=decodeAsBin(entropy64)
+        var bytes=HexstringToByteArray(hex)
+        var wordCount=12
+        const checksumBitCount = Math.floor(wordCount/3)
+	   
+        const totalBitCount = wordCount * 11
+        const generatedBitCount = totalBitCount - checksumBitCount
+        const generatedCharCount = Math.floor(generatedBitCount/4)
+        const entropyWithChecksum = getDecodedhash(bytes, generatedCharCount, checksumBitCount)
+        
+        console.log(bytes)
+        console.log(hex)
+       //console.log(hex2)
+        var words=pickWords(entropyWithChecksum) 
+        console.log(words)
+    }
+    function pickWords(entropyHash) {
+        var result = [];
+        const blen = entropyHash.length / 11;
+        for(var i=0; i<blen; i++) {
+            var idx = parseInt(entropyHash.substring(i * 11, (i + 1) * 11), 2);
+            result.push(bip39wordlist[idx]);
+        }
+        return result
+    }
+
+    function clearClassic() {
+        output = ''
+        document.getElementById("output").innerHTML = ''
+    }
+
+    function clearPalindromic() {
+        outputPal = ''
+        document.getElementById("outputPal").innerHTML = ''
+    }
+
+    var output = ''
+    var outputPal = ''
+    var __cfRLUnblockHandlers = 1 ;
+      
+    const bip39wordlist = [
+        "abandon",
+        "ability",
+        "able",
+        "about",
+        "above",
+        "absent",
+        "absorb",
+        "abstract",
+        "absurd",
+        "abuse",
+        "access",
+        "accident",
+        "account",
+        "accuse",
+        "achieve",
+        "acid",
+        "acoustic",
+        "acquire",
+        "across",
+        "act",
+        "action",
+        "actor",
+        "actress",
+        "actual",
+        "adapt",
+        "add",
+        "addict",
+        "address",
+        "adjust",
+        "admit",
+        "adult",
+        "advance",
+        "advice",
+        "aerobic",
+        "affair",
+        "afford",
+        "afraid",
+        "again",
+        "age",
+        "agent",
+        "agree",
+        "ahead",
+        "aim",
+        "air",
+        "airport",
+        "aisle",
+        "alarm",
+        "album",
+        "alcohol",
+        "alert",
+        "alien",
+        "all",
+        "alley",
+        "allow",
+        "almost",
+        "alone",
+        "alpha",
+        "already",
+        "also",
+        "alter",
+        "always",
+        "amateur",
+        "amazing",
+        "among",
+        "amount",
+        "amused",
+        "analyst",
+        "anchor",
+        "ancient",
+        "anger",
+        "angle",
+        "angry",
+        "animal",
+        "ankle",
+        "announce",
+        "annual",
+        "another",
+        "answer",
+        "antenna",
+        "antique",
+        "anxiety",
+        "any",
+        "apart",
+        "apology",
+        "appear",
+        "apple",
+        "approve",
+        "april",
+        "arch",
+        "arctic",
+        "area",
+        "arena",
+        "argue",
+        "arm",
+        "armed",
+        "armor",
+        "army",
+        "around",
+        "arrange",
+        "arrest",
+        "arrive",
+        "arrow",
+        "art",
+        "artefact",
+        "artist",
+        "artwork",
+        "ask",
+        "aspect",
+        "assault",
+        "asset",
+        "assist",
+        "assume",
+        "asthma",
+        "athlete",
+        "atom",
+        "attack",
+        "attend",
+        "attitude",
+        "attract",
+        "auction",
+        "audit",
+        "august",
+        "aunt",
+        "author",
+        "auto",
+        "autumn",
+        "average",
+        "avocado",
+        "avoid",
+        "awake",
+        "aware",
+        "away",
+        "awesome",
+        "awful",
+        "awkward",
+        "axis",
+        "baby",
+        "bachelor",
+        "bacon",
+        "badge",
+        "bag",
+        "balance",
+        "balcony",
+        "ball",
+        "bamboo",
+        "banana",
+        "banner",
+        "bar",
+        "barely",
+        "bargain",
+        "barrel",
+        "base",
+        "basic",
+        "basket",
+        "battle",
+        "beach",
+        "bean",
+        "beauty",
+        "because",
+        "become",
+        "beef",
+        "before",
+        "begin",
+        "behave",
+        "behind",
+        "believe",
+        "below",
+        "belt",
+        "bench",
+        "benefit",
+        "best",
+        "betray",
+        "better",
+        "between",
+        "beyond",
+        "bicycle",
+        "bid",
+        "bike",
+        "bind",
+        "biology",
+        "bird",
+        "birth",
+        "bitter",
+        "black",
+        "blade",
+        "blame",
+        "blanket",
+        "blast",
+        "bleak",
+        "bless",
+        "blind",
+        "blood",
+        "blossom",
+        "blouse",
+        "blue",
+        "blur",
+        "blush",
+        "board",
+        "boat",
+        "body",
+        "boil",
+        "bomb",
+        "bone",
+        "bonus",
+        "book",
+        "boost",
+        "border",
+        "boring",
+        "borrow",
+        "boss",
+        "bottom",
+        "bounce",
+        "box",
+        "boy",
+        "bracket",
+        "brain",
+        "brand",
+        "brass",
+        "brave",
+        "bread",
+        "breeze",
+        "brick",
+        "bridge",
+        "brief",
+        "bright",
+        "bring",
+        "brisk",
+        "broccoli",
+        "broken",
+        "bronze",
+        "broom",
+        "brother",
+        "brown",
+        "brush",
+        "bubble",
+        "buddy",
+        "budget",
+        "buffalo",
+        "build",
+        "bulb",
+        "bulk",
+        "bullet",
+        "bundle",
+        "bunker",
+        "burden",
+        "burger",
+        "burst",
+        "bus",
+        "business",
+        "busy",
+        "butter",
+        "buyer",
+        "buzz",
+        "cabbage",
+        "cabin",
+        "cable",
+        "cactus",
+        "cage",
+        "cake",
+        "call",
+        "calm",
+        "camera",
+        "camp",
+        "can",
+        "canal",
+        "cancel",
+        "candy",
+        "cannon",
+        "canoe",
+        "canvas",
+        "canyon",
+        "capable",
+        "capital",
+        "captain",
+        "car",
+        "carbon",
+        "card",
+        "cargo",
+        "carpet",
+        "carry",
+        "cart",
+        "case",
+        "cash",
+        "casino",
+        "castle",
+        "casual",
+        "cat",
+        "catalog",
+        "catch",
+        "category",
+        "cattle",
+        "caught",
+        "cause",
+        "caution",
+        "cave",
+        "ceiling",
+        "celery",
+        "cement",
+        "census",
+        "century",
+        "cereal",
+        "certain",
+        "chair",
+        "chalk",
+        "champion",
+        "change",
+        "chaos",
+        "chapter",
+        "charge",
+        "chase",
+        "chat",
+        "cheap",
+        "check",
+        "cheese",
+        "chef",
+        "cherry",
+        "chest",
+        "chicken",
+        "chief",
+        "child",
+        "chimney",
+        "choice",
+        "choose",
+        "chronic",
+        "chuckle",
+        "chunk",
+        "churn",
+        "cigar",
+        "cinnamon",
+        "circle",
+        "citizen",
+        "city",
+        "civil",
+        "claim",
+        "clap",
+        "clarify",
+        "claw",
+        "clay",
+        "clean",
+        "clerk",
+        "clever",
+        "click",
+        "client",
+        "cliff",
+        "climb",
+        "clinic",
+        "clip",
+        "clock",
+        "clog",
+        "close",
+        "cloth",
+        "cloud",
+        "clown",
+        "club",
+        "clump",
+        "cluster",
+        "clutch",
+        "coach",
+        "coast",
+        "coconut",
+        "code",
+        "coffee",
+        "coil",
+        "coin",
+        "collect",
+        "color",
+        "column",
+        "combine",
+        "come",
+        "comfort",
+        "comic",
+        "common",
+        "company",
+        "concert",
+        "conduct",
+        "confirm",
+        "congress",
+        "connect",
+        "consider",
+        "control",
+        "convince",
+        "cook",
+        "cool",
+        "copper",
+        "copy",
+        "coral",
+        "core",
+        "corn",
+        "correct",
+        "cost",
+        "cotton",
+        "couch",
+        "country",
+        "couple",
+        "course",
+        "cousin",
+        "cover",
+        "coyote",
+        "crack",
+        "cradle",
+        "craft",
+        "cram",
+        "crane",
+        "crash",
+        "crater",
+        "crawl",
+        "crazy",
+        "cream",
+        "credit",
+        "creek",
+        "crew",
+        "cricket",
+        "crime",
+        "crisp",
+        "critic",
+        "crop",
+        "cross",
+        "crouch",
+        "crowd",
+        "crucial",
+        "cruel",
+        "cruise",
+        "crumble",
+        "crunch",
+        "crush",
+        "cry",
+        "crystal",
+        "cube",
+        "culture",
+        "cup",
+        "cupboard",
+        "curious",
+        "current",
+        "curtain",
+        "curve",
+        "cushion",
+        "custom",
+        "cute",
+        "cycle",
+        "dad",
+        "damage",
+        "damp",
+        "dance",
+        "danger",
+        "daring",
+        "dash",
+        "daughter",
+        "dawn",
+        "day",
+        "deal",
+        "debate",
+        "debris",
+        "decade",
+        "december",
+        "decide",
+        "decline",
+        "decorate",
+        "decrease",
+        "deer",
+        "defense",
+        "define",
+        "defy",
+        "degree",
+        "delay",
+        "deliver",
+        "demand",
+        "demise",
+        "denial",
+        "dentist",
+        "deny",
+        "depart",
+        "depend",
+        "deposit",
+        "depth",
+        "deputy",
+        "derive",
+        "describe",
+        "desert",
+        "design",
+        "desk",
+        "despair",
+        "destroy",
+        "detail",
+        "detect",
+        "develop",
+        "device",
+        "devote",
+        "diagram",
+        "dial",
+        "diamond",
+        "diary",
+        "dice",
+        "diesel",
+        "diet",
+        "differ",
+        "digital",
+        "dignity",
+        "dilemma",
+        "dinner",
+        "dinosaur",
+        "direct",
+        "dirt",
+        "disagree",
+        "discover",
+        "disease",
+        "dish",
+        "dismiss",
+        "disorder",
+        "display",
+        "distance",
+        "divert",
+        "divide",
+        "divorce",
+        "dizzy",
+        "doctor",
+        "document",
+        "dog",
+        "doll",
+        "dolphin",
+        "domain",
+        "donate",
+        "donkey",
+        "donor",
+        "door",
+        "dose",
+        "double",
+        "dove",
+        "draft",
+        "dragon",
+        "drama",
+        "drastic",
+        "draw",
+        "dream",
+        "dress",
+        "drift",
+        "drill",
+        "drink",
+        "drip",
+        "drive",
+        "drop",
+        "drum",
+        "dry",
+        "duck",
+        "dumb",
+        "dune",
+        "during",
+        "dust",
+        "dutch",
+        "duty",
+        "dwarf",
+        "dynamic",
+        "eager",
+        "eagle",
+        "early",
+        "earn",
+        "earth",
+        "easily",
+        "east",
+        "easy",
+        "echo",
+        "ecology",
+        "economy",
+        "edge",
+        "edit",
+        "educate",
+        "effort",
+        "egg",
+        "eight",
+        "either",
+        "elbow",
+        "elder",
+        "electric",
+        "elegant",
+        "element",
+        "elephant",
+        "elevator",
+        "elite",
+        "else",
+        "embark",
+        "embody",
+        "embrace",
+        "emerge",
+        "emotion",
+        "employ",
+        "empower",
+        "empty",
+        "enable",
+        "enact",
+        "end",
+        "endless",
+        "endorse",
+        "enemy",
+        "energy",
+        "enforce",
+        "engage",
+        "engine",
+        "enhance",
+        "enjoy",
+        "enlist",
+        "enough",
+        "enrich",
+        "enroll",
+        "ensure",
+        "enter",
+        "entire",
+        "entry",
+        "envelope",
+        "episode",
+        "equal",
+        "equip",
+        "era",
+        "erase",
+        "erode",
+        "erosion",
+        "error",
+        "erupt",
+        "escape",
+        "essay",
+        "essence",
+        "estate",
+        "eternal",
+        "ethics",
+        "evidence",
+        "evil",
+        "evoke",
+        "evolve",
+        "exact",
+        "example",
+        "excess",
+        "exchange",
+        "excite",
+        "exclude",
+        "excuse",
+        "execute",
+        "exercise",
+        "exhaust",
+        "exhibit",
+        "exile",
+        "exist",
+        "exit",
+        "exotic",
+        "expand",
+        "expect",
+        "expire",
+        "explain",
+        "expose",
+        "express",
+        "extend",
+        "extra",
+        "eye",
+        "eyebrow",
+        "fabric",
+        "face",
+        "faculty",
+        "fade",
+        "faint",
+        "faith",
+        "fall",
+        "false",
+        "fame",
+        "family",
+        "famous",
+        "fan",
+        "fancy",
+        "fantasy",
+        "farm",
+        "fashion",
+        "fat",
+        "fatal",
+        "father",
+        "fatigue",
+        "fault",
+        "favorite",
+        "feature",
+        "february",
+        "federal",
+        "fee",
+        "feed",
+        "feel",
+        "female",
+        "fence",
+        "festival",
+        "fetch",
+        "fever",
+        "few",
+        "fiber",
+        "fiction",
+        "field",
+        "figure",
+        "file",
+        "film",
+        "filter",
+        "final",
+        "find",
+        "fine",
+        "finger",
+        "finish",
+        "fire",
+        "firm",
+        "first",
+        "fiscal",
+        "fish",
+        "fit",
+        "fitness",
+        "fix",
+        "flag",
+        "flame",
+        "flash",
+        "flat",
+        "flavor",
+        "flee",
+        "flight",
+        "flip",
+        "float",
+        "flock",
+        "floor",
+        "flower",
+        "fluid",
+        "flush",
+        "fly",
+        "foam",
+        "focus",
+        "fog",
+        "foil",
+        "fold",
+        "follow",
+        "food",
+        "foot",
+        "force",
+        "forest",
+        "forget",
+        "fork",
+        "fortune",
+        "forum",
+        "forward",
+        "fossil",
+        "foster",
+        "found",
+        "fox",
+        "fragile",
+        "frame",
+        "frequent",
+        "fresh",
+        "friend",
+        "fringe",
+        "frog",
+        "front",
+        "frost",
+        "frown",
+        "frozen",
+        "fruit",
+        "fuel",
+        "fun",
+        "funny",
+        "furnace",
+        "fury",
+        "future",
+        "gadget",
+        "gain",
+        "galaxy",
+        "gallery",
+        "game",
+        "gap",
+        "garage",
+        "garbage",
+        "garden",
+        "garlic",
+        "garment",
+        "gas",
+        "gasp",
+        "gate",
+        "gather",
+        "gauge",
+        "gaze",
+        "general",
+        "genius",
+        "genre",
+        "gentle",
+        "genuine",
+        "gesture",
+        "ghost",
+        "giant",
+        "gift",
+        "giggle",
+        "ginger",
+        "giraffe",
+        "girl",
+        "give",
+        "glad",
+        "glance",
+        "glare",
+        "glass",
+        "glide",
+        "glimpse",
+        "globe",
+        "gloom",
+        "glory",
+        "glove",
+        "glow",
+        "glue",
+        "goat",
+        "goddess",
+        "gold",
+        "good",
+        "goose",
+        "gorilla",
+        "gospel",
+        "gossip",
+        "govern",
+        "gown",
+        "grab",
+        "grace",
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+        "unfold",
+        "unhappy",
+        "uniform",
+        "unique",
+        "unit",
+        "universe",
+        "unknown",
+        "unlock",
+        "until",
+        "unusual",
+        "unveil",
+        "update",
+        "upgrade",
+        "uphold",
+        "upon",
+        "upper",
+        "upset",
+        "urban",
+        "urge",
+        "usage",
+        "use",
+        "used",
+        "useful",
+        "useless",
+        "usual",
+        "utility",
+        "vacant",
+        "vacuum",
+        "vague",
+        "valid",
+        "valley",
+        "valve",
+        "van",
+        "vanish",
+        "vapor",
+        "various",
+        "vast",
+        "vault",
+        "vehicle",
+        "velvet",
+        "vendor",
+        "venture",
+        "venue",
+        "verb",
+        "verify",
+        "version",
+        "very",
+        "vessel",
+        "veteran",
+        "viable",
+        "vibrant",
+        "vicious",
+        "victory",
+        "video",
+        "view",
+        "village",
+        "vintage",
+        "violin",
+        "virtual",
+        "virus",
+        "visa",
+        "visit",
+        "visual",
+        "vital",
+        "vivid",
+        "vocal",
+        "voice",
+        "void",
+        "volcano",
+        "volume",
+        "vote",
+        "voyage",
+        "wage",
+        "wagon",
+        "wait",
+        "walk",
+        "wall",
+        "walnut",
+        "want",
+        "warfare",
+        "warm",
+        "warrior",
+        "wash",
+        "wasp",
+        "waste",
+        "water",
+        "wave",
+        "way",
+        "wealth",
+        "weapon",
+        "wear",
+        "weasel",
+        "weather",
+        "web",
+        "wedding",
+        "weekend",
+        "weird",
+        "welcome",
+        "west",
+        "wet",
+        "whale",
+        "what",
+        "wheat",
+        "wheel",
+        "when",
+        "where",
+        "whip",
+        "whisper",
+        "wide",
+        "width",
+        "wife",
+        "wild",
+        "will",
+        "win",
+        "window",
+        "wine",
+        "wing",
+        "wink",
+        "winner",
+        "winter",
+        "wire",
+        "wisdom",
+        "wise",
+        "wish",
+        "witness",
+        "wolf",
+        "woman",
+        "wonder",
+        "wood",
+        "wool",
+        "word",
+        "work",
+        "world",
+        "worry",
+        "worth",
+        "wrap",
+        "wreck",
+        "wrestle",
+        "wrist",
+        "write",
+        "wrong",
+        "yard",
+        "year",
+        "yellow",
+        "you",
+        "young",
+        "youth",
+        "zebra",
+        "zero",
+        "zone",
+        "zoo"
+    ]
+    const base64library=["0",
+    "1",
+    "2",
+    "3",
+    "4",
+    "5",
+    "6",
+    "7",
+    "8",
+    "9",
+    "A",
+    "B",
+    "C",
+    "D",
+    "E",
+    "F",
+    "G",
+    "H",
+    "I",
+    "J",
+    "K",
+    "L",
+    "M",
+    "N",
+    "O",
+    "P",
+    "Q",
+    "R",
+    "S",
+    "T",
+    "U",
+    "V",
+    "W",
+    "X",
+    "Y",
+    "Z",
+    "!",
+    '"',
+    "#",
+    "$",
+    "%",
+    "&",
+    "'",
+    "(",
+    ")",
+    "*",
+    "+",
+    ",",
+    "-",
+    ".",
+    "{",
+    ":",
+    ";",
+    "<",
+    "=",
+    ">",
+    "?",
+    "@",
+    "[",
+    "}",
+    "]",
+    "^",
+    "_",
+    "`"]
+    var b64dict= {};
+    for(var i=0;i<base64library.length;i++) {
+        b64dict[base64library[i]] = i;
+    }
+
+    
+
+    function decodeAsBin(string) {
+        var output = [];
+        var s='';
+        for(var j=0;j<string.length;j++) {
+            if(string[j] != ' ') {
+                output.push(zfill(b64dict[string[j].toUpperCase()].toString(2), 6));
+            }
+        }
+        return output.join('');
+    }
+
+    function decodeAsHex(string) {
+    var bin = decodeAsBin(string);
+    var output = [];
+    var s='';
+    // Pad with 0 for binaries not divisible by 4, for hex conversion
+    var binModule = bin.length % 4;
+    if(binModule != 0) {
+        bin = zfill(bin, bin.length + 4 - binModule);
+    }
+    for(var i=0;i<bin.length;i=i+4) {
+        output.push(parseInt(bin.slice(i,i+4), 2).toString(16));
+    }
+    return output.join('');
+    }
+
+    function base64en(address_hex) {  // important never to rename base64en to "base64" which can corrupt the Python installation.
+    // (renamed alphabet to base64library below) alphabet = string.digits+string.ascii_uppercase+string.punctuation
+    
+    var b64_string = '';
+    // Convert hex to decimal
+    var x= new BigNumber(address_hex);
+    
+    // Append digits to the start of string
+    
+
+    while(x > 0) {
+       var digit = x.mod(64)
+	     //console.log(digit,'digit')
+       var digit_char = base64library[digit];
+         b64_string = digit_char + b64_string;
+        x =x.idiv(64)  ;
+	    //console.log(x,'new address int')    
+    }
+    return b64_string;
+}
+
+
+    </script>
+  </head>
+  <body>
+<h2>REGULAR: BIP39 Mnemonic Tool</h2>
+     <p>STEP 1: Select word count:</p>
+     <select id="wordLength">
+       <option value=12>SELECT 12 Words (128 bits of security)</option>
+       <option value=24>SELECT 24 Words (256 bits of security)</option>
+     </select>
+     <p>OPTIONAL: Insert entropy in the form of a 0x-padded hex string of length 32 (for 12 words) or 64 (for 24 words):</p>
+     <input id="entropy">
+     <br>
+     <br>
+     <button onclick="generateBIP39()"> STEP 2: Click Here to GENERATE (Mnemonic will appear below)</button>
+     <button onclick="clearClassic()">Click Here to CLEAR (Will Delete Data)</button>
+     <br>
+     <br>
+     <div id="output"></div>
+     <h2>REVERSIBLE: BIP39 Palindromic Mnemonic Tool</h2>
+     <p>STEP 1: Select word count:<p>
+     <select id="wordLengthPal">
+       <option value=12>SELECT 12 Words (128 bits of security)</option>
+       <option value=24>SELECT 24 Words (128 bits of security)</option>
+     </select>
+     <p>OPTIONAL: Insert entropy in the form of a 0x-padded hex string of length 32 (for 12 words) or 64 (for 24 words):</p>
+     <input id="entropyPal">
+     <br>
+     <br>
+     <button onclick="generateBIP39Palindromic()">STEP 2: Click Here to GENERATE Palindromic Mnemonic Words (Reversible Mnemonic will appear below)</button>
+     <button onclick="clearPalindromic()"> Click Here to CLEAR (Will Delete Data)</button>
+     <br>
+     <br>
+     <div id='outputPal'></div>
+     <h2>Decode Base64 Entropy </h2>
+     <input id="base64entropy">
+     <button onclick="Decrypt()"> Get Seed Words</button>
+     <br>
+     <br>
+  </body>
+</html>

From ec832de11fd2aefd2cc35800c325c21900a78d2b Mon Sep 17 00:00:00 2001
From: johhonn <35551051+johhonn@users.noreply.github.com>
Date: Tue, 30 Apr 2019 11:54:37 -0400
Subject: [PATCH 29/55] Update index.html

---
 index.html | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/index.html b/index.html
index 03f8b1a..9baa10e 100644
--- a/index.html
+++ b/index.html
@@ -377,6 +377,7 @@
        //console.log(hex2)
         var words=pickWords(entropyWithChecksum) 
         console.log(words)
+        document.getElementById('result').innerHTML=words
     }
     function pickWords(entropyHash) {
         var result = [];
@@ -2608,6 +2609,7 @@ <h2>Decode Base64 Entropy </h2>
      <input id="base64entropy">
      <button onclick="Decrypt()"> Get Seed Words</button>
      <br>
+     <p id='result'></p>
      <br>
   </body>
 </html>

From 21681a881502c63a5a584e18119274b4c2e55c89 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 11:57:16 -0400
Subject: [PATCH 30/55] Brought bignumber.js inline temporarily

---
 index.html | 2916 +++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 2915 insertions(+), 1 deletion(-)

diff --git a/index.html b/index.html
index 9baa10e..2da1e6e 100644
--- a/index.html
+++ b/index.html
@@ -64,7 +64,2921 @@
 b){var c={},d;for(d=0;d<b.length;d++)void 0!==a[b[d]]&&(c[b[d]]=a[b[d]]);return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.pa={};sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.pa,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=void 0===b.salt?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};
 "undefined"!==typeof module&&module.exports&&(module.exports=sjcl);"function"===typeof define&&define([],function(){return sjcl});
     </script>
-    <script src='./bignumber.js'></script>
+    //<script src='./bignumber.js'></script>
+	  
+	  <script name='bignumber.js'>
+  ;(function (globalObject) {
+  'use strict';
+
+/*
+ *      bignumber.js v8.1.1
+ *      A JavaScript library for arbitrary-precision arithmetic.
+ *      https://github.com/MikeMcl/bignumber.js
+ *      Copyright (c) 2019 Michael Mclaughlin <M8ch88l@gmail.com>
+ *      MIT Licensed.
+ *
+ *      BigNumber.prototype methods     |  BigNumber methods
+ *                                      |
+ *      absoluteValue            abs    |  clone
+ *      comparedTo                      |  config               set
+ *      decimalPlaces            dp     |      DECIMAL_PLACES
+ *      dividedBy                div    |      ROUNDING_MODE
+ *      dividedToIntegerBy       idiv   |      EXPONENTIAL_AT
+ *      exponentiatedBy          pow    |      RANGE
+ *      integerValue                    |      CRYPTO
+ *      isEqualTo                eq     |      MODULO_MODE
+ *      isFinite                        |      POW_PRECISION
+ *      isGreaterThan            gt     |      FORMAT
+ *      isGreaterThanOrEqualTo   gte    |      ALPHABET
+ *      isInteger                       |  isBigNumber
+ *      isLessThan               lt     |  maximum              max
+ *      isLessThanOrEqualTo      lte    |  minimum              min
+ *      isNaN                           |  random
+ *      isNegative                      |  sum
+ *      isPositive                      |
+ *      isZero                          |
+ *      minus                           |
+ *      modulo                   mod    |
+ *      multipliedBy             times  |
+ *      negated                         |
+ *      plus                            |
+ *      precision                sd     |
+ *      shiftedBy                       |
+ *      squareRoot               sqrt   |
+ *      toExponential                   |
+ *      toFixed                         |
+ *      toFormat                        |
+ *      toFraction                      |
+ *      toJSON                          |
+ *      toNumber                        |
+ *      toPrecision                     |
+ *      toString                        |
+ *      valueOf                         |
+ *
+ */
+
+
+  var BigNumber,
+    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
+    hasSymbol = typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol',
+
+    mathceil = Math.ceil,
+    mathfloor = Math.floor,
+
+    bignumberError = '[BigNumber Error] ',
+    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
+
+    BASE = 1e14,
+    LOG_BASE = 14,
+    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
+    // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
+    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
+    SQRT_BASE = 1e7,
+
+    // EDITABLE
+    // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
+    // the arguments to toExponential, toFixed, toFormat, and toPrecision.
+    MAX = 1E9;                                   // 0 to MAX_INT32
+
+
+  /*
+   * Create and return a BigNumber constructor.
+   */
+  function clone(configObject) {
+    var div, convertBase, parseNumeric,
+      P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
+      ONE = new BigNumber(1),
+
+
+      //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
+
+
+      // The default values below must be integers within the inclusive ranges stated.
+      // The values can also be changed at run-time using BigNumber.set.
+
+      // The maximum number of decimal places for operations involving division.
+      DECIMAL_PLACES = 20,                     // 0 to MAX
+
+      // The rounding mode used when rounding to the above decimal places, and when using
+      // toExponential, toFixed, toFormat and toPrecision, and round (default value).
+      // UP         0 Away from zero.
+      // DOWN       1 Towards zero.
+      // CEIL       2 Towards +Infinity.
+      // FLOOR      3 Towards -Infinity.
+      // HALF_UP    4 Towards nearest neighbour. If equidistant, up.
+      // HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
+      // HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
+      // HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
+      // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
+      ROUNDING_MODE = 4,                       // 0 to 8
+
+      // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
+
+      // The exponent value at and beneath which toString returns exponential notation.
+      // Number type: -7
+      TO_EXP_NEG = -7,                         // 0 to -MAX
+
+      // The exponent value at and above which toString returns exponential notation.
+      // Number type: 21
+      TO_EXP_POS = 21,                         // 0 to MAX
+
+      // RANGE : [MIN_EXP, MAX_EXP]
+
+      // The minimum exponent value, beneath which underflow to zero occurs.
+      // Number type: -324  (5e-324)
+      MIN_EXP = -1e7,                          // -1 to -MAX
+
+      // The maximum exponent value, above which overflow to Infinity occurs.
+      // Number type:  308  (1.7976931348623157e+308)
+      // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
+      MAX_EXP = 1e7,                           // 1 to MAX
+
+      // Whether to use cryptographically-secure random number generation, if available.
+      CRYPTO = false,                          // true or false
+
+      // The modulo mode used when calculating the modulus: a mod n.
+      // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
+      // The remainder (r) is calculated as: r = a - n * q.
+      //
+      // UP        0 The remainder is positive if the dividend is negative, else is negative.
+      // DOWN      1 The remainder has the same sign as the dividend.
+      //             This modulo mode is commonly known as 'truncated division' and is
+      //             equivalent to (a % n) in JavaScript.
+      // FLOOR     3 The remainder has the same sign as the divisor (Python %).
+      // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
+      // EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
+      //             The remainder is always positive.
+      //
+      // The truncated division, floored division, Euclidian division and IEEE 754 remainder
+      // modes are commonly used for the modulus operation.
+      // Although the other rounding modes can also be used, they may not give useful results.
+      MODULO_MODE = 1,                         // 0 to 9
+
+      // The maximum number of significant digits of the result of the exponentiatedBy operation.
+      // If POW_PRECISION is 0, there will be unlimited significant digits.
+      POW_PRECISION = 0,                    // 0 to MAX
+
+      // The format specification used by the BigNumber.prototype.toFormat method.
+      FORMAT = {
+        prefix: '',
+        groupSize: 3,
+        secondaryGroupSize: 0,
+        groupSeparator: ',',
+        decimalSeparator: '.',
+        fractionGroupSize: 0,
+        fractionGroupSeparator: '\xA0',      // non-breaking space
+        suffix: ''
+      },
+
+      // The alphabet used for base conversion. It must be at least 2 characters long, with no '+',
+      // '-', '.', whitespace, or repeated character.
+      // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+      ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
+
+
+    //------------------------------------------------------------------------------------------
+
+
+    // CONSTRUCTOR
+
+
+    /*
+     * The BigNumber constructor and exported function.
+     * Create and return a new instance of a BigNumber object.
+     *
+     * v {number|string|BigNumber} A numeric value.
+     * [b] {number} The base of v. Integer, 2 to ALPHABET.length inclusive.
+     */
+    function BigNumber(v, b) {
+      var alphabet, c, caseChanged, e, i, isNum, len, str,
+        x = this;
+
+      // Enable constructor call without `new`.
+      if (!(x instanceof BigNumber)) return new BigNumber(v, b);
+
+      if (b == null) {
+
+        if (v && v._isBigNumber === true) {
+          x.s = v.s;
+
+          if (!v.c || v.e > MAX_EXP) {
+            x.c = x.e = null;
+          } else if (v.e < MIN_EXP) {
+            x.c = [x.e = 0];
+          } else {
+            x.e = v.e;
+            x.c = v.c.slice();
+          }
+
+          return;
+        }
+
+        if ((isNum = typeof v == 'number') && v * 0 == 0) {
+
+          // Use `1 / n` to handle minus zero also.
+          x.s = 1 / v < 0 ? (v = -v, -1) : 1;
+
+          // Fast path for integers, where n < 2147483648 (2**31).
+          if (v === ~~v) {
+            for (e = 0, i = v; i >= 10; i /= 10, e++);
+
+            if (e > MAX_EXP) {
+              x.c = x.e = null;
+            } else {
+              x.e = e;
+              x.c = [v];
+            }
+
+            return;
+          }
+
+          str = String(v);
+        } else {
+
+          if (!isNumeric.test(str = String(v))) return parseNumeric(x, str, isNum);
+
+          x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
+        }
+
+        // Decimal point?
+        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+
+        // Exponential form?
+        if ((i = str.search(/e/i)) > 0) {
+
+          // Determine exponent.
+          if (e < 0) e = i;
+          e += +str.slice(i + 1);
+          str = str.substring(0, i);
+        } else if (e < 0) {
+
+          // Integer.
+          e = str.length;
+        }
+
+      } else {
+
+        // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+        intCheck(b, 2, ALPHABET.length, 'Base');
+
+        // Allow exponential notation to be used with base 10 argument, while
+        // also rounding to DECIMAL_PLACES as with other bases.
+        if (b == 10) {
+          x = new BigNumber(v);
+          return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
+        }
+
+        str = String(v);
+
+        if (isNum = typeof v == 'number') {
+
+          // Avoid potential interpretation of Infinity and NaN as base 44+ values.
+          if (v * 0 != 0) return parseNumeric(x, str, isNum, b);
+
+          x.s = 1 / v < 0 ? (str = str.slice(1), -1) : 1;
+
+          // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+          if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
+            throw Error
+             (tooManyDigits + v);
+          }
+        } else {
+          x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
+        }
+
+        alphabet = ALPHABET.slice(0, b);
+        e = i = 0;
+
+        // Check that str is a valid base b number.
+        // Don't use RegExp, so alphabet can contain special characters.
+        for (len = str.length; i < len; i++) {
+          if (alphabet.indexOf(c = str.charAt(i)) < 0) {
+            if (c == '.') {
+
+              // If '.' is not the first character and it has not be found before.
+              if (i > e) {
+                e = len;
+                continue;
+              }
+            } else if (!caseChanged) {
+
+              // Allow e.g. hexadecimal 'FF' as well as 'ff'.
+              if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
+                  str == str.toLowerCase() && (str = str.toUpperCase())) {
+                caseChanged = true;
+                i = -1;
+                e = 0;
+                continue;
+              }
+            }
+
+            return parseNumeric(x, String(v), isNum, b);
+          }
+        }
+
+        // Prevent later check for length on converted number.
+        isNum = false;
+        str = convertBase(str, b, 10, x.s);
+
+        // Decimal point?
+        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+        else e = str.length;
+      }
+
+      // Determine leading zeros.
+      for (i = 0; str.charCodeAt(i) === 48; i++);
+
+      // Determine trailing zeros.
+      for (len = str.length; str.charCodeAt(--len) === 48;);
+
+      if (str = str.slice(i, ++len)) {
+        len -= i;
+
+        // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+        if (isNum && BigNumber.DEBUG &&
+          len > 15 && (v > MAX_SAFE_INTEGER || v !== mathfloor(v))) {
+            throw Error
+             (tooManyDigits + (x.s * v));
+        }
+
+         // Overflow?
+        if ((e = e - i - 1) > MAX_EXP) {
+
+          // Infinity.
+          x.c = x.e = null;
+
+        // Underflow?
+        } else if (e < MIN_EXP) {
+
+          // Zero.
+          x.c = [x.e = 0];
+        } else {
+          x.e = e;
+          x.c = [];
+
+          // Transform base
+
+          // e is the base 10 exponent.
+          // i is where to slice str to get the first element of the coefficient array.
+          i = (e + 1) % LOG_BASE;
+          if (e < 0) i += LOG_BASE;  // i < 1
+
+          if (i < len) {
+            if (i) x.c.push(+str.slice(0, i));
+
+            for (len -= LOG_BASE; i < len;) {
+              x.c.push(+str.slice(i, i += LOG_BASE));
+            }
+
+            i = LOG_BASE - (str = str.slice(i)).length;
+          } else {
+            i -= len;
+          }
+
+          for (; i--; str += '0');
+          x.c.push(+str);
+        }
+      } else {
+
+        // Zero.
+        x.c = [x.e = 0];
+      }
+    }
+
+
+    // CONSTRUCTOR PROPERTIES
+
+
+    BigNumber.clone = clone;
+
+    BigNumber.ROUND_UP = 0;
+    BigNumber.ROUND_DOWN = 1;
+    BigNumber.ROUND_CEIL = 2;
+    BigNumber.ROUND_FLOOR = 3;
+    BigNumber.ROUND_HALF_UP = 4;
+    BigNumber.ROUND_HALF_DOWN = 5;
+    BigNumber.ROUND_HALF_EVEN = 6;
+    BigNumber.ROUND_HALF_CEIL = 7;
+    BigNumber.ROUND_HALF_FLOOR = 8;
+    BigNumber.EUCLID = 9;
+
+
+    /*
+     * Configure infrequently-changing library-wide settings.
+     *
+     * Accept an object with the following optional properties (if the value of a property is
+     * a number, it must be an integer within the inclusive range stated):
+     *
+     *   DECIMAL_PLACES   {number}           0 to MAX
+     *   ROUNDING_MODE    {number}           0 to 8
+     *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
+     *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
+     *   CRYPTO           {boolean}          true or false
+     *   MODULO_MODE      {number}           0 to 9
+     *   POW_PRECISION       {number}           0 to MAX
+     *   ALPHABET         {string}           A string of two or more unique characters which does
+     *                                       not contain '.'.
+     *   FORMAT           {object}           An object with some of the following properties:
+     *     prefix                 {string}
+     *     groupSize              {number}
+     *     secondaryGroupSize     {number}
+     *     groupSeparator         {string}
+     *     decimalSeparator       {string}
+     *     fractionGroupSize      {number}
+     *     fractionGroupSeparator {string}
+     *     suffix                 {string}
+     *
+     * (The values assigned to the above FORMAT object properties are not checked for validity.)
+     *
+     * E.g.
+     * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
+     *
+     * Ignore properties/parameters set to null or undefined, except for ALPHABET.
+     *
+     * Return an object with the properties current values.
+     */
+    BigNumber.config = BigNumber.set = function (obj) {
+      var p, v;
+
+      if (obj != null) {
+
+        if (typeof obj == 'object') {
+
+          // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
+          // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
+            v = obj[p];
+            intCheck(v, 0, MAX, p);
+            DECIMAL_PLACES = v;
+          }
+
+          // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
+          // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
+            v = obj[p];
+            intCheck(v, 0, 8, p);
+            ROUNDING_MODE = v;
+          }
+
+          // EXPONENTIAL_AT {number|number[]}
+          // Integer, -MAX to MAX inclusive or
+          // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
+          // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
+            v = obj[p];
+            if (v && v.pop) {
+              intCheck(v[0], -MAX, 0, p);
+              intCheck(v[1], 0, MAX, p);
+              TO_EXP_NEG = v[0];
+              TO_EXP_POS = v[1];
+            } else {
+              intCheck(v, -MAX, MAX, p);
+              TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
+            }
+          }
+
+          // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
+          // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
+          // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
+          if (obj.hasOwnProperty(p = 'RANGE')) {
+            v = obj[p];
+            if (v && v.pop) {
+              intCheck(v[0], -MAX, -1, p);
+              intCheck(v[1], 1, MAX, p);
+              MIN_EXP = v[0];
+              MAX_EXP = v[1];
+            } else {
+              intCheck(v, -MAX, MAX, p);
+              if (v) {
+                MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
+              } else {
+                throw Error
+                 (bignumberError + p + ' cannot be zero: ' + v);
+              }
+            }
+          }
+
+          // CRYPTO {boolean} true or false.
+          // '[BigNumber Error] CRYPTO not true or false: {v}'
+          // '[BigNumber Error] crypto unavailable'
+          if (obj.hasOwnProperty(p = 'CRYPTO')) {
+            v = obj[p];
+            if (v === !!v) {
+              if (v) {
+                if (typeof crypto != 'undefined' && crypto &&
+                 (crypto.getRandomValues || crypto.randomBytes)) {
+                  CRYPTO = v;
+                } else {
+                  CRYPTO = !v;
+                  throw Error
+                   (bignumberError + 'crypto unavailable');
+                }
+              } else {
+                CRYPTO = v;
+              }
+            } else {
+              throw Error
+               (bignumberError + p + ' not true or false: ' + v);
+            }
+          }
+
+          // MODULO_MODE {number} Integer, 0 to 9 inclusive.
+          // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
+            v = obj[p];
+            intCheck(v, 0, 9, p);
+            MODULO_MODE = v;
+          }
+
+          // POW_PRECISION {number} Integer, 0 to MAX inclusive.
+          // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
+            v = obj[p];
+            intCheck(v, 0, MAX, p);
+            POW_PRECISION = v;
+          }
+
+          // FORMAT {object}
+          // '[BigNumber Error] FORMAT not an object: {v}'
+          if (obj.hasOwnProperty(p = 'FORMAT')) {
+            v = obj[p];
+            if (typeof v == 'object') FORMAT = v;
+            else throw Error
+             (bignumberError + p + ' not an object: ' + v);
+          }
+
+          // ALPHABET {string}
+          // '[BigNumber Error] ALPHABET invalid: {v}'
+          if (obj.hasOwnProperty(p = 'ALPHABET')) {
+            v = obj[p];
+
+            // Disallow if only one character,
+            // or if it contains '+', '-', '.', whitespace, or a repeated character.
+            if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
+              ALPHABET = v;
+            } else {
+              throw Error
+               (bignumberError + p + ' invalid: ' + v);
+            }
+          }
+
+        } else {
+
+          // '[BigNumber Error] Object expected: {v}'
+          throw Error
+           (bignumberError + 'Object expected: ' + obj);
+        }
+      }
+
+      return {
+        DECIMAL_PLACES: DECIMAL_PLACES,
+        ROUNDING_MODE: ROUNDING_MODE,
+        EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
+        RANGE: [MIN_EXP, MAX_EXP],
+        CRYPTO: CRYPTO,
+        MODULO_MODE: MODULO_MODE,
+        POW_PRECISION: POW_PRECISION,
+        FORMAT: FORMAT,
+        ALPHABET: ALPHABET
+      };
+    };
+
+
+    /*
+     * Return true if v is a BigNumber instance, otherwise return false.
+     *
+     * If BigNumber.DEBUG is true, throw if a BigNumber instance is not well-formed.
+     *
+     * v {any}
+     *
+     * '[BigNumber Error] Invalid BigNumber: {v}'
+     */
+    BigNumber.isBigNumber = function (v) {
+      if (!v || v._isBigNumber !== true) return false;
+      if (!BigNumber.DEBUG) return true;
+
+      var i, n,
+        c = v.c,
+        e = v.e,
+        s = v.s;
+
+      out: if ({}.toString.call(c) == '[object Array]') {
+
+        if ((s === 1 || s === -1) && e >= -MAX && e <= MAX && e === mathfloor(e)) {
+
+          // If the first element is zero, the BigNumber value must be zero.
+          if (c[0] === 0) {
+            if (e === 0 && c.length === 1) return true;
+            break out;
+          }
+
+          // Calculate number of digits that c[0] should have, based on the exponent.
+          i = (e + 1) % LOG_BASE;
+          if (i < 1) i += LOG_BASE;
+
+          // Calculate number of digits of c[0].
+          //if (Math.ceil(Math.log(c[0] + 1) / Math.LN10) == i) {
+          if (String(c[0]).length == i) {
+
+            for (i = 0; i < c.length; i++) {
+              n = c[i];
+              if (n < 0 || n >= BASE || n !== mathfloor(n)) break out;
+            }
+
+            // Last element cannot be zero, unless it is the only element.
+            if (n !== 0) return true;
+          }
+        }
+
+      // Infinity/NaN
+      } else if (c === null && e === null && (s === null || s === 1 || s === -1)) {
+        return true;
+      }
+
+      throw Error
+        (bignumberError + 'Invalid BigNumber: ' + v);
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the maximum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.maximum = BigNumber.max = function () {
+      return maxOrMin(arguments, P.lt);
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the minimum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.minimum = BigNumber.min = function () {
+      return maxOrMin(arguments, P.gt);
+    };
+
+
+    /*
+     * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
+     * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
+     * zeros are produced).
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
+     * '[BigNumber Error] crypto unavailable'
+     */
+    BigNumber.random = (function () {
+      var pow2_53 = 0x20000000000000;
+
+      // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
+      // Check if Math.random() produces more than 32 bits of randomness.
+      // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
+      // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
+      var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
+       ? function () { return mathfloor(Math.random() * pow2_53); }
+       : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
+         (Math.random() * 0x800000 | 0); };
+
+      return function (dp) {
+        var a, b, e, k, v,
+          i = 0,
+          c = [],
+          rand = new BigNumber(ONE);
+
+        if (dp == null) dp = DECIMAL_PLACES;
+        else intCheck(dp, 0, MAX);
+
+        k = mathceil(dp / LOG_BASE);
+
+        if (CRYPTO) {
+
+          // Browsers supporting crypto.getRandomValues.
+          if (crypto.getRandomValues) {
+
+            a = crypto.getRandomValues(new Uint32Array(k *= 2));
+
+            for (; i < k;) {
+
+              // 53 bits:
+              // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
+              // 11111 11111111 11111111 11111111 11100000 00000000 00000000
+              // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
+              //                                     11111 11111111 11111111
+              // 0x20000 is 2^21.
+              v = a[i] * 0x20000 + (a[i + 1] >>> 11);
+
+              // Rejection sampling:
+              // 0 <= v < 9007199254740992
+              // Probability that v >= 9e15, is
+              // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
+              if (v >= 9e15) {
+                b = crypto.getRandomValues(new Uint32Array(2));
+                a[i] = b[0];
+                a[i + 1] = b[1];
+              } else {
+
+                // 0 <= v <= 8999999999999999
+                // 0 <= (v % 1e14) <= 99999999999999
+                c.push(v % 1e14);
+                i += 2;
+              }
+            }
+            i = k / 2;
+
+          // Node.js supporting crypto.randomBytes.
+          } else if (crypto.randomBytes) {
+
+            // buffer
+            a = crypto.randomBytes(k *= 7);
+
+            for (; i < k;) {
+
+              // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
+              // 0x100000000 is 2^32, 0x1000000 is 2^24
+              // 11111 11111111 11111111 11111111 11111111 11111111 11111111
+              // 0 <= v < 9007199254740992
+              v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
+                 (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
+                 (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
+
+              if (v >= 9e15) {
+                crypto.randomBytes(7).copy(a, i);
+              } else {
+
+                // 0 <= (v % 1e14) <= 99999999999999
+                c.push(v % 1e14);
+                i += 7;
+              }
+            }
+            i = k / 7;
+          } else {
+            CRYPTO = false;
+            throw Error
+             (bignumberError + 'crypto unavailable');
+          }
+        }
+
+        // Use Math.random.
+        if (!CRYPTO) {
+
+          for (; i < k;) {
+            v = random53bitInt();
+            if (v < 9e15) c[i++] = v % 1e14;
+          }
+        }
+
+        k = c[--i];
+        dp %= LOG_BASE;
+
+        // Convert trailing digits to zeros according to dp.
+        if (k && dp) {
+          v = POWS_TEN[LOG_BASE - dp];
+          c[i] = mathfloor(k / v) * v;
+        }
+
+        // Remove trailing elements which are zero.
+        for (; c[i] === 0; c.pop(), i--);
+
+        // Zero?
+        if (i < 0) {
+          c = [e = 0];
+        } else {
+
+          // Remove leading elements which are zero and adjust exponent accordingly.
+          for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
+
+          // Count the digits of the first element of c to determine leading zeros, and...
+          for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
+
+          // adjust the exponent accordingly.
+          if (i < LOG_BASE) e -= LOG_BASE - i;
+        }
+
+        rand.e = e;
+        rand.c = c;
+        return rand;
+      };
+    })();
+
+
+    /*
+     * Return a BigNumber whose value is the sum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.sum = function () {
+      var i = 1,
+        args = arguments,
+        sum = new BigNumber(args[0]);
+      for (; i < args.length;) sum = sum.plus(args[i++]);
+      return sum;
+    };
+
+
+    // PRIVATE FUNCTIONS
+
+
+    // Called by BigNumber and BigNumber.prototype.toString.
+    convertBase = (function () {
+      var decimal = '0123456789';
+
+      /*
+       * Convert string of baseIn to an array of numbers of baseOut.
+       * Eg. toBaseOut('255', 10, 16) returns [15, 15].
+       * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
+       */
+      function toBaseOut(str, baseIn, baseOut, alphabet) {
+        var j,
+          arr = [0],
+          arrL,
+          i = 0,
+          len = str.length;
+
+        for (; i < len;) {
+          for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
+
+          arr[0] += alphabet.indexOf(str.charAt(i++));
+
+          for (j = 0; j < arr.length; j++) {
+
+            if (arr[j] > baseOut - 1) {
+              if (arr[j + 1] == null) arr[j + 1] = 0;
+              arr[j + 1] += arr[j] / baseOut | 0;
+              arr[j] %= baseOut;
+            }
+          }
+        }
+
+        return arr.reverse();
+      }
+
+      // Convert a numeric string of baseIn to a numeric string of baseOut.
+      // If the caller is toString, we are converting from base 10 to baseOut.
+      // If the caller is BigNumber, we are converting from baseIn to base 10.
+      return function (str, baseIn, baseOut, sign, callerIsToString) {
+        var alphabet, d, e, k, r, x, xc, y,
+          i = str.indexOf('.'),
+          dp = DECIMAL_PLACES,
+          rm = ROUNDING_MODE;
+
+        // Non-integer.
+        if (i >= 0) {
+          k = POW_PRECISION;
+
+          // Unlimited precision.
+          POW_PRECISION = 0;
+          str = str.replace('.', '');
+          y = new BigNumber(baseIn);
+          x = y.pow(str.length - i);
+          POW_PRECISION = k;
+
+          // Convert str as if an integer, then restore the fraction part by dividing the
+          // result by its base raised to a power.
+
+          y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
+           10, baseOut, decimal);
+          y.e = y.c.length;
+        }
+
+        // Convert the number as integer.
+
+        xc = toBaseOut(str, baseIn, baseOut, callerIsToString
+         ? (alphabet = ALPHABET, decimal)
+         : (alphabet = decimal, ALPHABET));
+
+        // xc now represents str as an integer and converted to baseOut. e is the exponent.
+        e = k = xc.length;
+
+        // Remove trailing zeros.
+        for (; xc[--k] == 0; xc.pop());
+
+        // Zero?
+        if (!xc[0]) return alphabet.charAt(0);
+
+        // Does str represent an integer? If so, no need for the division.
+        if (i < 0) {
+          --e;
+        } else {
+          x.c = xc;
+          x.e = e;
+
+          // The sign is needed for correct rounding.
+          x.s = sign;
+          x = div(x, y, dp, rm, baseOut);
+          xc = x.c;
+          r = x.r;
+          e = x.e;
+        }
+
+        // xc now represents str converted to baseOut.
+
+        // THe index of the rounding digit.
+        d = e + dp + 1;
+
+        // The rounding digit: the digit to the right of the digit that may be rounded up.
+        i = xc[d];
+
+        // Look at the rounding digits and mode to determine whether to round up.
+
+        k = baseOut / 2;
+        r = r || d < 0 || xc[d + 1] != null;
+
+        r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+              : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
+               rm == (x.s < 0 ? 8 : 7));
+
+        // If the index of the rounding digit is not greater than zero, or xc represents
+        // zero, then the result of the base conversion is zero or, if rounding up, a value
+        // such as 0.00001.
+        if (d < 1 || !xc[0]) {
+
+          // 1^-dp or 0
+          str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
+        } else {
+
+          // Truncate xc to the required number of decimal places.
+          xc.length = d;
+
+          // Round up?
+          if (r) {
+
+            // Rounding up may mean the previous digit has to be rounded up and so on.
+            for (--baseOut; ++xc[--d] > baseOut;) {
+              xc[d] = 0;
+
+              if (!d) {
+                ++e;
+                xc = [1].concat(xc);
+              }
+            }
+          }
+
+          // Determine trailing zeros.
+          for (k = xc.length; !xc[--k];);
+
+          // E.g. [4, 11, 15] becomes 4bf.
+          for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
+
+          // Add leading zeros, decimal point and trailing zeros as required.
+          str = toFixedPoint(str, e, alphabet.charAt(0));
+        }
+
+        // The caller will add the sign.
+        return str;
+      };
+    })();
+
+
+    // Perform division in the specified base. Called by div and convertBase.
+    div = (function () {
+
+      // Assume non-zero x and k.
+      function multiply(x, k, base) {
+        var m, temp, xlo, xhi,
+          carry = 0,
+          i = x.length,
+          klo = k % SQRT_BASE,
+          khi = k / SQRT_BASE | 0;
+
+        for (x = x.slice(); i--;) {
+          xlo = x[i] % SQRT_BASE;
+          xhi = x[i] / SQRT_BASE | 0;
+          m = khi * xlo + xhi * klo;
+          temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
+          carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
+          x[i] = temp % base;
+        }
+
+        if (carry) x = [carry].concat(x);
+
+        return x;
+      }
+
+      function compare(a, b, aL, bL) {
+        var i, cmp;
+
+        if (aL != bL) {
+          cmp = aL > bL ? 1 : -1;
+        } else {
+
+          for (i = cmp = 0; i < aL; i++) {
+
+            if (a[i] != b[i]) {
+              cmp = a[i] > b[i] ? 1 : -1;
+              break;
+            }
+          }
+        }
+
+        return cmp;
+      }
+
+      function subtract(a, b, aL, base) {
+        var i = 0;
+
+        // Subtract b from a.
+        for (; aL--;) {
+          a[aL] -= i;
+          i = a[aL] < b[aL] ? 1 : 0;
+          a[aL] = i * base + a[aL] - b[aL];
+        }
+
+        // Remove leading zeros.
+        for (; !a[0] && a.length > 1; a.splice(0, 1));
+      }
+
+      // x: dividend, y: divisor.
+      return function (x, y, dp, rm, base) {
+        var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
+          yL, yz,
+          s = x.s == y.s ? 1 : -1,
+          xc = x.c,
+          yc = y.c;
+
+        // Either NaN, Infinity or 0?
+        if (!xc || !xc[0] || !yc || !yc[0]) {
+
+          return new BigNumber(
+
+           // Return NaN if either NaN, or both Infinity or 0.
+           !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
+
+            // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
+            xc && xc[0] == 0 || !yc ? s * 0 : s / 0
+         );
+        }
+
+        q = new BigNumber(s);
+        qc = q.c = [];
+        e = x.e - y.e;
+        s = dp + e + 1;
+
+        if (!base) {
+          base = BASE;
+          e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
+          s = s / LOG_BASE | 0;
+        }
+
+        // Result exponent may be one less then the current value of e.
+        // The coefficients of the BigNumbers from convertBase may have trailing zeros.
+        for (i = 0; yc[i] == (xc[i] || 0); i++);
+
+        if (yc[i] > (xc[i] || 0)) e--;
+
+        if (s < 0) {
+          qc.push(1);
+          more = true;
+        } else {
+          xL = xc.length;
+          yL = yc.length;
+          i = 0;
+          s += 2;
+
+          // Normalise xc and yc so highest order digit of yc is >= base / 2.
+
+          n = mathfloor(base / (yc[0] + 1));
+
+          // Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
+          // if (n > 1 || n++ == 1 && yc[0] < base / 2) {
+          if (n > 1) {
+            yc = multiply(yc, n, base);
+            xc = multiply(xc, n, base);
+            yL = yc.length;
+            xL = xc.length;
+          }
+
+          xi = yL;
+          rem = xc.slice(0, yL);
+          remL = rem.length;
+
+          // Add zeros to make remainder as long as divisor.
+          for (; remL < yL; rem[remL++] = 0);
+          yz = yc.slice();
+          yz = [0].concat(yz);
+          yc0 = yc[0];
+          if (yc[1] >= base / 2) yc0++;
+          // Not necessary, but to prevent trial digit n > base, when using base 3.
+          // else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
+
+          do {
+            n = 0;
+
+            // Compare divisor and remainder.
+            cmp = compare(yc, rem, yL, remL);
+
+            // If divisor < remainder.
+            if (cmp < 0) {
+
+              // Calculate trial digit, n.
+
+              rem0 = rem[0];
+              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
+
+              // n is how many times the divisor goes into the current remainder.
+              n = mathfloor(rem0 / yc0);
+
+              //  Algorithm:
+              //  product = divisor multiplied by trial digit (n).
+              //  Compare product and remainder.
+              //  If product is greater than remainder:
+              //    Subtract divisor from product, decrement trial digit.
+              //  Subtract product from remainder.
+              //  If product was less than remainder at the last compare:
+              //    Compare new remainder and divisor.
+              //    If remainder is greater than divisor:
+              //      Subtract divisor from remainder, increment trial digit.
+
+              if (n > 1) {
+
+                // n may be > base only when base is 3.
+                if (n >= base) n = base - 1;
+
+                // product = divisor * trial digit.
+                prod = multiply(yc, n, base);
+                prodL = prod.length;
+                remL = rem.length;
+
+                // Compare product and remainder.
+                // If product > remainder then trial digit n too high.
+                // n is 1 too high about 5% of the time, and is not known to have
+                // ever been more than 1 too high.
+                while (compare(prod, rem, prodL, remL) == 1) {
+                  n--;
+
+                  // Subtract divisor from product.
+                  subtract(prod, yL < prodL ? yz : yc, prodL, base);
+                  prodL = prod.length;
+                  cmp = 1;
+                }
+              } else {
+
+                // n is 0 or 1, cmp is -1.
+                // If n is 0, there is no need to compare yc and rem again below,
+                // so change cmp to 1 to avoid it.
+                // If n is 1, leave cmp as -1, so yc and rem are compared again.
+                if (n == 0) {
+
+                  // divisor < remainder, so n must be at least 1.
+                  cmp = n = 1;
+                }
+
+                // product = divisor
+                prod = yc.slice();
+                prodL = prod.length;
+              }
+
+              if (prodL < remL) prod = [0].concat(prod);
+
+              // Subtract product from remainder.
+              subtract(rem, prod, remL, base);
+              remL = rem.length;
+
+               // If product was < remainder.
+              if (cmp == -1) {
+
+                // Compare divisor and new remainder.
+                // If divisor < new remainder, subtract divisor from remainder.
+                // Trial digit n too low.
+                // n is 1 too low about 5% of the time, and very rarely 2 too low.
+                while (compare(yc, rem, yL, remL) < 1) {
+                  n++;
+
+                  // Subtract divisor from remainder.
+                  subtract(rem, yL < remL ? yz : yc, remL, base);
+                  remL = rem.length;
+                }
+              }
+            } else if (cmp === 0) {
+              n++;
+              rem = [0];
+            } // else cmp === 1 and n will be 0
+
+            // Add the next digit, n, to the result array.
+            qc[i++] = n;
+
+            // Update the remainder.
+            if (rem[0]) {
+              rem[remL++] = xc[xi] || 0;
+            } else {
+              rem = [xc[xi]];
+              remL = 1;
+            }
+          } while ((xi++ < xL || rem[0] != null) && s--);
+
+          more = rem[0] != null;
+
+          // Leading zero?
+          if (!qc[0]) qc.splice(0, 1);
+        }
+
+        if (base == BASE) {
+
+          // To calculate q.e, first get the number of digits of qc[0].
+          for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
+
+          round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
+
+        // Caller is convertBase.
+        } else {
+          q.e = e;
+          q.r = +more;
+        }
+
+        return q;
+      };
+    })();
+
+
+    /*
+     * Return a string representing the value of BigNumber n in fixed-point or exponential
+     * notation rounded to the specified decimal places or significant digits.
+     *
+     * n: a BigNumber.
+     * i: the index of the last digit required (i.e. the digit that may be rounded up).
+     * rm: the rounding mode.
+     * id: 1 (toExponential) or 2 (toPrecision).
+     */
+    function format(n, i, rm, id) {
+      var c0, e, ne, len, str;
+
+      if (rm == null) rm = ROUNDING_MODE;
+      else intCheck(rm, 0, 8);
+
+      if (!n.c) return n.toString();
+
+      c0 = n.c[0];
+      ne = n.e;
+
+      if (i == null) {
+        str = coeffToString(n.c);
+        str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
+         ? toExponential(str, ne)
+         : toFixedPoint(str, ne, '0');
+      } else {
+        n = round(new BigNumber(n), i, rm);
+
+        // n.e may have changed if the value was rounded up.
+        e = n.e;
+
+        str = coeffToString(n.c);
+        len = str.length;
+
+        // toPrecision returns exponential notation if the number of significant digits
+        // specified is less than the number of digits necessary to represent the integer
+        // part of the value in fixed-point notation.
+
+        // Exponential notation.
+        if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
+
+          // Append zeros?
+          for (; len < i; str += '0', len++);
+          str = toExponential(str, e);
+
+        // Fixed-point notation.
+        } else {
+          i -= ne;
+          str = toFixedPoint(str, e, '0');
+
+          // Append zeros?
+          if (e + 1 > len) {
+            if (--i > 0) for (str += '.'; i--; str += '0');
+          } else {
+            i += e - len;
+            if (i > 0) {
+              if (e + 1 == len) str += '.';
+              for (; i--; str += '0');
+            }
+          }
+        }
+      }
+
+      return n.s < 0 && c0 ? '-' + str : str;
+    }
+
+
+    // Handle BigNumber.max and BigNumber.min.
+    function maxOrMin(args, method) {
+      var n,
+        i = 1,
+        m = new BigNumber(args[0]);
+
+      for (; i < args.length; i++) {
+        n = new BigNumber(args[i]);
+
+        // If any number is NaN, return NaN.
+        if (!n.s) {
+          m = n;
+          break;
+        } else if (method.call(m, n)) {
+          m = n;
+        }
+      }
+
+      return m;
+    }
+
+
+    /*
+     * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
+     * Called by minus, plus and times.
+     */
+    function normalise(n, c, e) {
+      var i = 1,
+        j = c.length;
+
+       // Remove trailing zeros.
+      for (; !c[--j]; c.pop());
+
+      // Calculate the base 10 exponent. First get the number of digits of c[0].
+      for (j = c[0]; j >= 10; j /= 10, i++);
+
+      // Overflow?
+      if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
+
+        // Infinity.
+        n.c = n.e = null;
+
+      // Underflow?
+      } else if (e < MIN_EXP) {
+
+        // Zero.
+        n.c = [n.e = 0];
+      } else {
+        n.e = e;
+        n.c = c;
+      }
+
+      return n;
+    }
+
+
+    // Handle values that fail the validity test in BigNumber.
+    parseNumeric = (function () {
+      var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
+        dotAfter = /^([^.]+)\.$/,
+        dotBefore = /^\.([^.]+)$/,
+        isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+        whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+
+      return function (x, str, isNum, b) {
+        var base,
+          s = isNum ? str : str.replace(whitespaceOrPlus, '');
+
+        // No exception on ±Infinity or NaN.
+        if (isInfinityOrNaN.test(s)) {
+          x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
+        } else {
+          if (!isNum) {
+
+            // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
+            s = s.replace(basePrefix, function (m, p1, p2) {
+              base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
+              return !b || b == base ? p1 : m;
+            });
+
+            if (b) {
+              base = b;
+
+              // E.g. '1.' to '1', '.1' to '0.1'
+              s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
+            }
+
+            if (str != s) return new BigNumber(s, base);
+          }
+
+          // '[BigNumber Error] Not a number: {n}'
+          // '[BigNumber Error] Not a base {b} number: {n}'
+          if (BigNumber.DEBUG) {
+            throw Error
+              (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
+          }
+
+          // NaN
+          x.s = null;
+        }
+
+        x.c = x.e = null;
+      }
+    })();
+
+
+    /*
+     * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
+     * If r is truthy, it is known that there are more digits after the rounding digit.
+     */
+    function round(x, sd, rm, r) {
+      var d, i, j, k, n, ni, rd,
+        xc = x.c,
+        pows10 = POWS_TEN;
+
+      // if x is not Infinity or NaN...
+      if (xc) {
+
+        // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
+        // n is a base 1e14 number, the value of the element of array x.c containing rd.
+        // ni is the index of n within x.c.
+        // d is the number of digits of n.
+        // i is the index of rd within n including leading zeros.
+        // j is the actual index of rd within n (if < 0, rd is a leading zero).
+        out: {
+
+          // Get the number of digits of the first element of xc.
+          for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
+          i = sd - d;
+
+          // If the rounding digit is in the first element of xc...
+          if (i < 0) {
+            i += LOG_BASE;
+            j = sd;
+            n = xc[ni = 0];
+
+            // Get the rounding digit at index j of n.
+            rd = n / pows10[d - j - 1] % 10 | 0;
+          } else {
+            ni = mathceil((i + 1) / LOG_BASE);
+
+            if (ni >= xc.length) {
+
+              if (r) {
+
+                // Needed by sqrt.
+                for (; xc.length <= ni; xc.push(0));
+                n = rd = 0;
+                d = 1;
+                i %= LOG_BASE;
+                j = i - LOG_BASE + 1;
+              } else {
+                break out;
+              }
+            } else {
+              n = k = xc[ni];
+
+              // Get the number of digits of n.
+              for (d = 1; k >= 10; k /= 10, d++);
+
+              // Get the index of rd within n.
+              i %= LOG_BASE;
+
+              // Get the index of rd within n, adjusted for leading zeros.
+              // The number of leading zeros of n is given by LOG_BASE - d.
+              j = i - LOG_BASE + d;
+
+              // Get the rounding digit at index j of n.
+              rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
+            }
+          }
+
+          r = r || sd < 0 ||
+
+          // Are there any non-zero digits after the rounding digit?
+          // The expression  n % pows10[d - j - 1]  returns all digits of n to the right
+          // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
+           xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
+
+          r = rm < 4
+           ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+           : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
+
+            // Check whether the digit to the left of the rounding digit is odd.
+            ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
+             rm == (x.s < 0 ? 8 : 7));
+
+          if (sd < 1 || !xc[0]) {
+            xc.length = 0;
+
+            if (r) {
+
+              // Convert sd to decimal places.
+              sd -= x.e + 1;
+
+              // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+              xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
+              x.e = -sd || 0;
+            } else {
+
+              // Zero.
+              xc[0] = x.e = 0;
+            }
+
+            return x;
+          }
+
+          // Remove excess digits.
+          if (i == 0) {
+            xc.length = ni;
+            k = 1;
+            ni--;
+          } else {
+            xc.length = ni + 1;
+            k = pows10[LOG_BASE - i];
+
+            // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+            // j > 0 means i > number of leading zeros of n.
+            xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
+          }
+
+          // Round up?
+          if (r) {
+
+            for (; ;) {
+
+              // If the digit to be rounded up is in the first element of xc...
+              if (ni == 0) {
+
+                // i will be the length of xc[0] before k is added.
+                for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
+                j = xc[0] += k;
+                for (k = 1; j >= 10; j /= 10, k++);
+
+                // if i != k the length has increased.
+                if (i != k) {
+                  x.e++;
+                  if (xc[0] == BASE) xc[0] = 1;
+                }
+
+                break;
+              } else {
+                xc[ni] += k;
+                if (xc[ni] != BASE) break;
+                xc[ni--] = 0;
+                k = 1;
+              }
+            }
+          }
+
+          // Remove trailing zeros.
+          for (i = xc.length; xc[--i] === 0; xc.pop());
+        }
+
+        // Overflow? Infinity.
+        if (x.e > MAX_EXP) {
+          x.c = x.e = null;
+
+        // Underflow? Zero.
+        } else if (x.e < MIN_EXP) {
+          x.c = [x.e = 0];
+        }
+      }
+
+      return x;
+    }
+
+
+    function valueOf(n) {
+      var str,
+        e = n.e;
+
+      if (e === null) return n.toString();
+
+      str = coeffToString(n.c);
+
+      str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+        ? toExponential(str, e)
+        : toFixedPoint(str, e, '0');
+
+      return n.s < 0 ? '-' + str : str;
+    }
+
+
+    // PROTOTYPE/INSTANCE METHODS
+
+
+    /*
+     * Return a new BigNumber whose value is the absolute value of this BigNumber.
+     */
+    P.absoluteValue = P.abs = function () {
+      var x = new BigNumber(this);
+      if (x.s < 0) x.s = 1;
+      return x;
+    };
+
+
+    /*
+     * Return
+     *   1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
+     *   -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
+     *   0 if they have the same value,
+     *   or null if the value of either is NaN.
+     */
+    P.comparedTo = function (y, b) {
+      return compare(this, new BigNumber(y, b));
+    };
+
+
+    /*
+     * If dp is undefined or null or true or false, return the number of decimal places of the
+     * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+     *
+     * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
+     * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
+     * ROUNDING_MODE if rm is omitted.
+     *
+     * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.decimalPlaces = P.dp = function (dp, rm) {
+      var c, n, v,
+        x = this;
+
+      if (dp != null) {
+        intCheck(dp, 0, MAX);
+        if (rm == null) rm = ROUNDING_MODE;
+        else intCheck(rm, 0, 8);
+
+        return round(new BigNumber(x), dp + x.e + 1, rm);
+      }
+
+      if (!(c = x.c)) return null;
+      n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
+
+      // Subtract the number of trailing zeros of the last number.
+      if (v = c[v]) for (; v % 10 == 0; v /= 10, n--);
+      if (n < 0) n = 0;
+
+      return n;
+    };
+
+
+    /*
+     *  n / 0 = I
+     *  n / N = N
+     *  n / I = 0
+     *  0 / n = 0
+     *  0 / 0 = N
+     *  0 / N = N
+     *  0 / I = 0
+     *  N / n = N
+     *  N / 0 = N
+     *  N / N = N
+     *  N / I = N
+     *  I / n = I
+     *  I / 0 = I
+     *  I / N = N
+     *  I / I = N
+     *
+     * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
+     * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+     */
+    P.dividedBy = P.div = function (y, b) {
+      return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the integer part of dividing the value of this
+     * BigNumber by the value of BigNumber(y, b).
+     */
+    P.dividedToIntegerBy = P.idiv = function (y, b) {
+      return div(this, new BigNumber(y, b), 0, 1);
+    };
+
+
+    /*
+     * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
+     *
+     * If m is present, return the result modulo m.
+     * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
+     * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
+     *
+     * The modular power operation works efficiently when x, n, and m are integers, otherwise it
+     * is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
+     *
+     * n {number|string|BigNumber} The exponent. An integer.
+     * [m] {number|string|BigNumber} The modulus.
+     *
+     * '[BigNumber Error] Exponent not an integer: {n}'
+     */
+    P.exponentiatedBy = P.pow = function (n, m) {
+      var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
+        x = this;
+
+      n = new BigNumber(n);
+
+      // Allow NaN and ±Infinity, but not other non-integers.
+      if (n.c && !n.isInteger()) {
+        throw Error
+          (bignumberError + 'Exponent not an integer: ' + valueOf(n));
+      }
+
+      if (m != null) m = new BigNumber(m);
+
+      // Exponent of MAX_SAFE_INTEGER is 15.
+      nIsBig = n.e > 14;
+
+      // If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
+      if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
+
+        // The sign of the result of pow when x is negative depends on the evenness of n.
+        // If +n overflows to ±Infinity, the evenness of n would be not be known.
+        y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
+        return m ? y.mod(m) : y;
+      }
+
+      nIsNeg = n.s < 0;
+
+      if (m) {
+
+        // x % m returns NaN if abs(m) is zero, or m is NaN.
+        if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
+
+        isModExp = !nIsNeg && x.isInteger() && m.isInteger();
+
+        if (isModExp) x = x.mod(m);
+
+      // Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
+      // Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
+      } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
+        // [1, 240000000]
+        ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
+        // [80000000000000]  [99999750000000]
+        : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
+
+        // If x is negative and n is odd, k = -0, else k = 0.
+        k = x.s < 0 && isOdd(n) ? -0 : 0;
+
+        // If x >= 1, k = ±Infinity.
+        if (x.e > -1) k = 1 / k;
+
+        // If n is negative return ±0, else return ±Infinity.
+        return new BigNumber(nIsNeg ? 1 / k : k);
+
+      } else if (POW_PRECISION) {
+
+        // Truncating each coefficient array to a length of k after each multiplication
+        // equates to truncating significant digits to POW_PRECISION + [28, 41],
+        // i.e. there will be a minimum of 28 guard digits retained.
+        k = mathceil(POW_PRECISION / LOG_BASE + 2);
+      }
+
+      if (nIsBig) {
+        half = new BigNumber(0.5);
+        if (nIsNeg) n.s = 1;
+        nIsOdd = isOdd(n);
+      } else {
+        i = Math.abs(+valueOf(n));
+        nIsOdd = i % 2;
+      }
+
+      y = new BigNumber(ONE);
+
+      // Performs 54 loop iterations for n of 9007199254740991.
+      for (; ;) {
+
+        if (nIsOdd) {
+          y = y.times(x);
+          if (!y.c) break;
+
+          if (k) {
+            if (y.c.length > k) y.c.length = k;
+          } else if (isModExp) {
+            y = y.mod(m);    //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
+          }
+        }
+
+        if (i) {
+          i = mathfloor(i / 2);
+          if (i === 0) break;
+          nIsOdd = i % 2;
+        } else {
+          n = n.times(half);
+          round(n, n.e + 1, 1);
+
+          if (n.e > 14) {
+            nIsOdd = isOdd(n);
+          } else {
+            i = +valueOf(n);
+            if (i === 0) break;
+            nIsOdd = i % 2;
+          }
+        }
+
+        x = x.times(x);
+
+        if (k) {
+          if (x.c && x.c.length > k) x.c.length = k;
+        } else if (isModExp) {
+          x = x.mod(m);    //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
+        }
+      }
+
+      if (isModExp) return y;
+      if (nIsNeg) y = ONE.div(y);
+
+      return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
+     * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+     *
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
+     */
+    P.integerValue = function (rm) {
+      var n = new BigNumber(this);
+      if (rm == null) rm = ROUNDING_MODE;
+      else intCheck(rm, 0, 8);
+      return round(n, n.e + 1, rm);
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isEqualTo = P.eq = function (y, b) {
+      return compare(this, new BigNumber(y, b)) === 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is a finite number, otherwise return false.
+     */
+    P.isFinite = function () {
+      return !!this.c;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isGreaterThan = P.gt = function (y, b) {
+      return compare(this, new BigNumber(y, b)) > 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is greater than or equal to the value of
+     * BigNumber(y, b), otherwise return false.
+     */
+    P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
+      return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
+
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is an integer, otherwise return false.
+     */
+    P.isInteger = function () {
+      return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isLessThan = P.lt = function (y, b) {
+      return compare(this, new BigNumber(y, b)) < 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is less than or equal to the value of
+     * BigNumber(y, b), otherwise return false.
+     */
+    P.isLessThanOrEqualTo = P.lte = function (y, b) {
+      return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is NaN, otherwise return false.
+     */
+    P.isNaN = function () {
+      return !this.s;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is negative, otherwise return false.
+     */
+    P.isNegative = function () {
+      return this.s < 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is positive, otherwise return false.
+     */
+    P.isPositive = function () {
+      return this.s > 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
+     */
+    P.isZero = function () {
+      return !!this.c && this.c[0] == 0;
+    };
+
+
+    /*
+     *  n - 0 = n
+     *  n - N = N
+     *  n - I = -I
+     *  0 - n = -n
+     *  0 - 0 = 0
+     *  0 - N = N
+     *  0 - I = -I
+     *  N - n = N
+     *  N - 0 = N
+     *  N - N = N
+     *  N - I = N
+     *  I - n = I
+     *  I - 0 = I
+     *  I - N = N
+     *  I - I = N
+     *
+     * Return a new BigNumber whose value is the value of this BigNumber minus the value of
+     * BigNumber(y, b).
+     */
+    P.minus = function (y, b) {
+      var i, j, t, xLTy,
+        x = this,
+        a = x.s;
+
+      y = new BigNumber(y, b);
+      b = y.s;
+
+      // Either NaN?
+      if (!a || !b) return new BigNumber(NaN);
+
+      // Signs differ?
+      if (a != b) {
+        y.s = -b;
+        return x.plus(y);
+      }
+
+      var xe = x.e / LOG_BASE,
+        ye = y.e / LOG_BASE,
+        xc = x.c,
+        yc = y.c;
+
+      if (!xe || !ye) {
+
+        // Either Infinity?
+        if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
+
+        // Either zero?
+        if (!xc[0] || !yc[0]) {
+
+          // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+          return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
+
+           // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
+           ROUNDING_MODE == 3 ? -0 : 0);
+        }
+      }
+
+      xe = bitFloor(xe);
+      ye = bitFloor(ye);
+      xc = xc.slice();
+
+      // Determine which is the bigger number.
+      if (a = xe - ye) {
+
+        if (xLTy = a < 0) {
+          a = -a;
+          t = xc;
+        } else {
+          ye = xe;
+          t = yc;
+        }
+
+        t.reverse();
+
+        // Prepend zeros to equalise exponents.
+        for (b = a; b--; t.push(0));
+        t.reverse();
+      } else {
+
+        // Exponents equal. Check digit by digit.
+        j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
+
+        for (a = b = 0; b < j; b++) {
+
+          if (xc[b] != yc[b]) {
+            xLTy = xc[b] < yc[b];
+            break;
+          }
+        }
+      }
+
+      // x < y? Point xc to the array of the bigger number.
+      if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
+
+      b = (j = yc.length) - (i = xc.length);
+
+      // Append zeros to xc if shorter.
+      // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
+      if (b > 0) for (; b--; xc[i++] = 0);
+      b = BASE - 1;
+
+      // Subtract yc from xc.
+      for (; j > a;) {
+
+        if (xc[--j] < yc[j]) {
+          for (i = j; i && !xc[--i]; xc[i] = b);
+          --xc[i];
+          xc[j] += BASE;
+        }
+
+        xc[j] -= yc[j];
+      }
+
+      // Remove leading zeros and adjust exponent accordingly.
+      for (; xc[0] == 0; xc.splice(0, 1), --ye);
+
+      // Zero?
+      if (!xc[0]) {
+
+        // Following IEEE 754 (2008) 6.3,
+        // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
+        y.s = ROUNDING_MODE == 3 ? -1 : 1;
+        y.c = [y.e = 0];
+        return y;
+      }
+
+      // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
+      // for finite x and y.
+      return normalise(y, xc, ye);
+    };
+
+
+    /*
+     *   n % 0 =  N
+     *   n % N =  N
+     *   n % I =  n
+     *   0 % n =  0
+     *  -0 % n = -0
+     *   0 % 0 =  N
+     *   0 % N =  N
+     *   0 % I =  0
+     *   N % n =  N
+     *   N % 0 =  N
+     *   N % N =  N
+     *   N % I =  N
+     *   I % n =  N
+     *   I % 0 =  N
+     *   I % N =  N
+     *   I % I =  N
+     *
+     * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
+     * BigNumber(y, b). The result depends on the value of MODULO_MODE.
+     */
+    P.modulo = P.mod = function (y, b) {
+      var q, s,
+        x = this;
+
+      y = new BigNumber(y, b);
+
+      // Return NaN if x is Infinity or NaN, or y is NaN or zero.
+      if (!x.c || !y.s || y.c && !y.c[0]) {
+        return new BigNumber(NaN);
+
+      // Return x if y is Infinity or x is zero.
+      } else if (!y.c || x.c && !x.c[0]) {
+        return new BigNumber(x);
+      }
+
+      if (MODULO_MODE == 9) {
+
+        // Euclidian division: q = sign(y) * floor(x / abs(y))
+        // r = x - qy    where  0 <= r < abs(y)
+        s = y.s;
+        y.s = 1;
+        q = div(x, y, 0, 3);
+        y.s = s;
+        q.s *= s;
+      } else {
+        q = div(x, y, 0, MODULO_MODE);
+      }
+
+      y = x.minus(q.times(y));
+
+      // To match JavaScript %, ensure sign of zero is sign of dividend.
+      if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
+
+      return y;
+    };
+
+
+    /*
+     *  n * 0 = 0
+     *  n * N = N
+     *  n * I = I
+     *  0 * n = 0
+     *  0 * 0 = 0
+     *  0 * N = N
+     *  0 * I = N
+     *  N * n = N
+     *  N * 0 = N
+     *  N * N = N
+     *  N * I = N
+     *  I * n = I
+     *  I * 0 = N
+     *  I * N = N
+     *  I * I = I
+     *
+     * Return a new BigNumber whose value is the value of this BigNumber multiplied by the value
+     * of BigNumber(y, b).
+     */
+    P.multipliedBy = P.times = function (y, b) {
+      var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
+        base, sqrtBase,
+        x = this,
+        xc = x.c,
+        yc = (y = new BigNumber(y, b)).c;
+
+      // Either NaN, ±Infinity or ±0?
+      if (!xc || !yc || !xc[0] || !yc[0]) {
+
+        // Return NaN if either is NaN, or one is 0 and the other is Infinity.
+        if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
+          y.c = y.e = y.s = null;
+        } else {
+          y.s *= x.s;
+
+          // Return ±Infinity if either is ±Infinity.
+          if (!xc || !yc) {
+            y.c = y.e = null;
+
+          // Return ±0 if either is ±0.
+          } else {
+            y.c = [0];
+            y.e = 0;
+          }
+        }
+
+        return y;
+      }
+
+      e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
+      y.s *= x.s;
+      xcL = xc.length;
+      ycL = yc.length;
+
+      // Ensure xc points to longer array and xcL to its length.
+      if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
+
+      // Initialise the result array with zeros.
+      for (i = xcL + ycL, zc = []; i--; zc.push(0));
+
+      base = BASE;
+      sqrtBase = SQRT_BASE;
+
+      for (i = ycL; --i >= 0;) {
+        c = 0;
+        ylo = yc[i] % sqrtBase;
+        yhi = yc[i] / sqrtBase | 0;
+
+        for (k = xcL, j = i + k; j > i;) {
+          xlo = xc[--k] % sqrtBase;
+          xhi = xc[k] / sqrtBase | 0;
+          m = yhi * xlo + xhi * ylo;
+          xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
+          c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
+          zc[j--] = xlo % base;
+        }
+
+        zc[j] = c;
+      }
+
+      if (c) {
+        ++e;
+      } else {
+        zc.splice(0, 1);
+      }
+
+      return normalise(y, zc, e);
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber negated,
+     * i.e. multiplied by -1.
+     */
+    P.negated = function () {
+      var x = new BigNumber(this);
+      x.s = -x.s || null;
+      return x;
+    };
+
+
+    /*
+     *  n + 0 = n
+     *  n + N = N
+     *  n + I = I
+     *  0 + n = n
+     *  0 + 0 = 0
+     *  0 + N = N
+     *  0 + I = I
+     *  N + n = N
+     *  N + 0 = N
+     *  N + N = N
+     *  N + I = N
+     *  I + n = I
+     *  I + 0 = I
+     *  I + N = N
+     *  I + I = I
+     *
+     * Return a new BigNumber whose value is the value of this BigNumber plus the value of
+     * BigNumber(y, b).
+     */
+    P.plus = function (y, b) {
+      var t,
+        x = this,
+        a = x.s;
+
+      y = new BigNumber(y, b);
+      b = y.s;
+
+      // Either NaN?
+      if (!a || !b) return new BigNumber(NaN);
+
+      // Signs differ?
+       if (a != b) {
+        y.s = -b;
+        return x.minus(y);
+      }
+
+      var xe = x.e / LOG_BASE,
+        ye = y.e / LOG_BASE,
+        xc = x.c,
+        yc = y.c;
+
+      if (!xe || !ye) {
+
+        // Return ±Infinity if either ±Infinity.
+        if (!xc || !yc) return new BigNumber(a / 0);
+
+        // Either zero?
+        // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+        if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
+      }
+
+      xe = bitFloor(xe);
+      ye = bitFloor(ye);
+      xc = xc.slice();
+
+      // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
+      if (a = xe - ye) {
+        if (a > 0) {
+          ye = xe;
+          t = yc;
+        } else {
+          a = -a;
+          t = xc;
+        }
+
+        t.reverse();
+        for (; a--; t.push(0));
+        t.reverse();
+      }
+
+      a = xc.length;
+      b = yc.length;
+
+      // Point xc to the longer array, and b to the shorter length.
+      if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
+
+      // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
+      for (a = 0; b;) {
+        a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
+        xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
+      }
+
+      if (a) {
+        xc = [a].concat(xc);
+        ++ye;
+      }
+
+      // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+      // ye = MAX_EXP + 1 possible
+      return normalise(y, xc, ye);
+    };
+
+
+    /*
+     * If sd is undefined or null or true or false, return the number of significant digits of
+     * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+     * If sd is true include integer-part trailing zeros in the count.
+     *
+     * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
+     * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
+     * ROUNDING_MODE if rm is omitted.
+     *
+     * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
+     *                     boolean: whether to count integer-part trailing zeros: true or false.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+     */
+    P.precision = P.sd = function (sd, rm) {
+      var c, n, v,
+        x = this;
+
+      if (sd != null && sd !== !!sd) {
+        intCheck(sd, 1, MAX);
+        if (rm == null) rm = ROUNDING_MODE;
+        else intCheck(rm, 0, 8);
+
+        return round(new BigNumber(x), sd, rm);
+      }
+
+      if (!(c = x.c)) return null;
+      v = c.length - 1;
+      n = v * LOG_BASE + 1;
+
+      if (v = c[v]) {
+
+        // Subtract the number of trailing zeros of the last element.
+        for (; v % 10 == 0; v /= 10, n--);
+
+        // Add the number of digits of the first element.
+        for (v = c[0]; v >= 10; v /= 10, n++);
+      }
+
+      if (sd && x.e + 1 > n) n = x.e + 1;
+
+      return n;
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
+     * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
+     *
+     * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
+     */
+    P.shiftedBy = function (k) {
+      intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
+      return this.times('1e' + k);
+    };
+
+
+    /*
+     *  sqrt(-n) =  N
+     *  sqrt(N) =  N
+     *  sqrt(-I) =  N
+     *  sqrt(I) =  I
+     *  sqrt(0) =  0
+     *  sqrt(-0) = -0
+     *
+     * Return a new BigNumber whose value is the square root of the value of this BigNumber,
+     * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+     */
+    P.squareRoot = P.sqrt = function () {
+      var m, n, r, rep, t,
+        x = this,
+        c = x.c,
+        s = x.s,
+        e = x.e,
+        dp = DECIMAL_PLACES + 4,
+        half = new BigNumber('0.5');
+
+      // Negative/NaN/Infinity/zero?
+      if (s !== 1 || !c || !c[0]) {
+        return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
+      }
+
+      // Initial estimate.
+      s = Math.sqrt(+valueOf(x));
+
+      // Math.sqrt underflow/overflow?
+      // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+      if (s == 0 || s == 1 / 0) {
+        n = coeffToString(c);
+        if ((n.length + e) % 2 == 0) n += '0';
+        s = Math.sqrt(+n);
+        e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);
+
+        if (s == 1 / 0) {
+          n = '1e' + e;
+        } else {
+          n = s.toExponential();
+          n = n.slice(0, n.indexOf('e') + 1) + e;
+        }
+
+        r = new BigNumber(n);
+      } else {
+        r = new BigNumber(s + '');
+      }
+
+      // Check for zero.
+      // r could be zero if MIN_EXP is changed after the this value was created.
+      // This would cause a division by zero (x/t) and hence Infinity below, which would cause
+      // coeffToString to throw.
+      if (r.c[0]) {
+        e = r.e;
+        s = e + dp;
+        if (s < 3) s = 0;
+
+        // Newton-Raphson iteration.
+        for (; ;) {
+          t = r;
+          r = half.times(t.plus(div(x, t, dp, 1)));
+
+          if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
+
+            // The exponent of r may here be one less than the final result exponent,
+            // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
+            // are indexed correctly.
+            if (r.e < e) --s;
+            n = n.slice(s - 3, s + 1);
+
+            // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
+            // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
+            // iteration.
+            if (n == '9999' || !rep && n == '4999') {
+
+              // On the first iteration only, check to see if rounding up gives the
+              // exact result as the nines may infinitely repeat.
+              if (!rep) {
+                round(t, t.e + DECIMAL_PLACES + 2, 0);
+
+                if (t.times(t).eq(x)) {
+                  r = t;
+                  break;
+                }
+              }
+
+              dp += 4;
+              s += 4;
+              rep = 1;
+            } else {
+
+              // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
+              // result. If not, then there are further digits and m will be truthy.
+              if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
+
+                // Truncate to the first rounding digit.
+                round(r, r.e + DECIMAL_PLACES + 2, 1);
+                m = !r.times(r).eq(x);
+              }
+
+              break;
+            }
+          }
+        }
+      }
+
+      return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in exponential notation and
+     * rounded using ROUNDING_MODE to dp fixed decimal places.
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toExponential = function (dp, rm) {
+      if (dp != null) {
+        intCheck(dp, 0, MAX);
+        dp++;
+      }
+      return format(this, dp, rm, 1);
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in fixed-point notation rounding
+     * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+     *
+     * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
+     * but e.g. (-0.00001).toFixed(0) is '-0'.
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toFixed = function (dp, rm) {
+      if (dp != null) {
+        intCheck(dp, 0, MAX);
+        dp = dp + this.e + 1;
+      }
+      return format(this, dp, rm);
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in fixed-point notation rounded
+     * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
+     * of the format or FORMAT object (see BigNumber.set).
+     *
+     * The formatting object may contain some or all of the properties shown below.
+     *
+     * FORMAT = {
+     *   prefix: '',
+     *   groupSize: 3,
+     *   secondaryGroupSize: 0,
+     *   groupSeparator: ',',
+     *   decimalSeparator: '.',
+     *   fractionGroupSize: 0,
+     *   fractionGroupSeparator: '\xA0',      // non-breaking space
+     *   suffix: ''
+     * };
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     * [format] {object} Formatting options. See FORMAT pbject above.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     * '[BigNumber Error] Argument not an object: {format}'
+     */
+    P.toFormat = function (dp, rm, format) {
+      var str,
+        x = this;
+
+      if (format == null) {
+        if (dp != null && rm && typeof rm == 'object') {
+          format = rm;
+          rm = null;
+        } else if (dp && typeof dp == 'object') {
+          format = dp;
+          dp = rm = null;
+        } else {
+          format = FORMAT;
+        }
+      } else if (typeof format != 'object') {
+        throw Error
+          (bignumberError + 'Argument not an object: ' + format);
+      }
+
+      str = x.toFixed(dp, rm);
+
+      if (x.c) {
+        var i,
+          arr = str.split('.'),
+          g1 = +format.groupSize,
+          g2 = +format.secondaryGroupSize,
+          groupSeparator = format.groupSeparator || '',
+          intPart = arr[0],
+          fractionPart = arr[1],
+          isNeg = x.s < 0,
+          intDigits = isNeg ? intPart.slice(1) : intPart,
+          len = intDigits.length;
+
+        if (g2) i = g1, g1 = g2, g2 = i, len -= i;
+
+        if (g1 > 0 && len > 0) {
+          i = len % g1 || g1;
+          intPart = intDigits.substr(0, i);
+          for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
+          if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
+          if (isNeg) intPart = '-' + intPart;
+        }
+
+        str = fractionPart
+         ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
+          ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
+           '$&' + (format.fractionGroupSeparator || ''))
+          : fractionPart)
+         : intPart;
+      }
+
+      return (format.prefix || '') + str + (format.suffix || '');
+    };
+
+
+    /*
+     * Return an array of two BigNumbers representing the value of this BigNumber as a simple
+     * fraction with an integer numerator and an integer denominator.
+     * The denominator will be a positive non-zero value less than or equal to the specified
+     * maximum denominator. If a maximum denominator is not specified, the denominator will be
+     * the lowest value necessary to represent the number exactly.
+     *
+     * [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
+     *
+     * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
+     */
+    P.toFraction = function (md) {
+      var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
+        x = this,
+        xc = x.c;
+
+      if (md != null) {
+        n = new BigNumber(md);
+
+        // Throw if md is less than one or is not an integer, unless it is Infinity.
+        if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
+          throw Error
+            (bignumberError + 'Argument ' +
+              (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
+        }
+      }
+
+      if (!xc) return new BigNumber(x);
+
+      d = new BigNumber(ONE);
+      n1 = d0 = new BigNumber(ONE);
+      d1 = n0 = new BigNumber(ONE);
+      s = coeffToString(xc);
+
+      // Determine initial denominator.
+      // d is a power of 10 and the minimum max denominator that specifies the value exactly.
+      e = d.e = s.length - x.e - 1;
+      d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
+      md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
+
+      exp = MAX_EXP;
+      MAX_EXP = 1 / 0;
+      n = new BigNumber(s);
+
+      // n0 = d1 = 0
+      n0.c[0] = 0;
+
+      for (; ;)  {
+        q = div(n, d, 0, 1);
+        d2 = d0.plus(q.times(d1));
+        if (d2.comparedTo(md) == 1) break;
+        d0 = d1;
+        d1 = d2;
+        n1 = n0.plus(q.times(d2 = n1));
+        n0 = d2;
+        d = n.minus(q.times(d2 = d));
+        n = d2;
+      }
+
+      d2 = div(md.minus(d0), d1, 0, 1);
+      n0 = n0.plus(d2.times(n1));
+      d0 = d0.plus(d2.times(d1));
+      n0.s = n1.s = x.s;
+      e = e * 2;
+
+      // Determine which fraction is closer to x, n0/d0 or n1/d1
+      r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
+          div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
+
+      MAX_EXP = exp;
+
+      return r;
+    };
+
+
+    /*
+     * Return the value of this BigNumber converted to a number primitive.
+     */
+    P.toNumber = function () {
+      return +valueOf(this);
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber rounded to sd significant digits
+     * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
+     * necessary to represent the integer part of the value in fixed-point notation, then use
+     * exponential notation.
+     *
+     * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+     */
+    P.toPrecision = function (sd, rm) {
+      if (sd != null) intCheck(sd, 1, MAX);
+      return format(this, sd, rm, 2);
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in base b, or base 10 if b is
+     * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
+     * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
+     * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
+     * TO_EXP_NEG, return exponential notation.
+     *
+     * [b] {number} Integer, 2 to ALPHABET.length inclusive.
+     *
+     * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+     */
+    P.toString = function (b) {
+      var str,
+        n = this,
+        s = n.s,
+        e = n.e;
+
+      // Infinity or NaN?
+      if (e === null) {
+        if (s) {
+          str = 'Infinity';
+          if (s < 0) str = '-' + str;
+        } else {
+          str = 'NaN';
+        }
+      } else {
+        if (b == null) {
+          str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+           ? toExponential(coeffToString(n.c), e)
+           : toFixedPoint(coeffToString(n.c), e, '0');
+        } else if (b === 10) {
+          n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
+          str = toFixedPoint(coeffToString(n.c), n.e, '0');
+        } else {
+          intCheck(b, 2, ALPHABET.length, 'Base');
+          str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
+        }
+
+        if (s < 0 && n.c[0]) str = '-' + str;
+      }
+
+      return str;
+    };
+
+
+    /*
+     * Return as toString, but do not accept a base argument, and include the minus sign for
+     * negative zero.
+     */
+    P.valueOf = P.toJSON = function () {
+      return valueOf(this);
+    };
+
+
+    P._isBigNumber = true;
+
+    if (hasSymbol) {
+      P[Symbol.toStringTag] = 'BigNumber';
+
+      // Node.js v10.12.0+
+      P[Symbol.for('nodejs.util.inspect.custom')] = P.valueOf;
+    }
+
+    if (configObject != null) BigNumber.set(configObject);
+
+    return BigNumber;
+  }
+
+
+  // PRIVATE HELPER FUNCTIONS
+
+  // These functions don't need access to variables,
+  // e.g. DECIMAL_PLACES, in the scope of the `clone` function above.
+
+
+  function bitFloor(n) {
+    var i = n | 0;
+    return n > 0 || n === i ? i : i - 1;
+  }
+
+
+  // Return a coefficient array as a string of base 10 digits.
+  function coeffToString(a) {
+    var s, z,
+      i = 1,
+      j = a.length,
+      r = a[0] + '';
+
+    for (; i < j;) {
+      s = a[i++] + '';
+      z = LOG_BASE - s.length;
+      for (; z--; s = '0' + s);
+      r += s;
+    }
+
+    // Determine trailing zeros.
+    for (j = r.length; r.charCodeAt(--j) === 48;);
+
+    return r.slice(0, j + 1 || 1);
+  }
+
+
+  // Compare the value of BigNumbers x and y.
+  function compare(x, y) {
+    var a, b,
+      xc = x.c,
+      yc = y.c,
+      i = x.s,
+      j = y.s,
+      k = x.e,
+      l = y.e;
+
+    // Either NaN?
+    if (!i || !j) return null;
+
+    a = xc && !xc[0];
+    b = yc && !yc[0];
+
+    // Either zero?
+    if (a || b) return a ? b ? 0 : -j : i;
+
+    // Signs differ?
+    if (i != j) return i;
+
+    a = i < 0;
+    b = k == l;
+
+    // Either Infinity?
+    if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
+
+    // Compare exponents.
+    if (!b) return k > l ^ a ? 1 : -1;
+
+    j = (k = xc.length) < (l = yc.length) ? k : l;
+
+    // Compare digit by digit.
+    for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
+
+    // Compare lengths.
+    return k == l ? 0 : k > l ^ a ? 1 : -1;
+  }
+
+
+  /*
+   * Check that n is a primitive number, an integer, and in range, otherwise throw.
+   */
+  function intCheck(n, min, max, name) {
+    if (n < min || n > max || n !== mathfloor(n)) {
+      throw Error
+       (bignumberError + (name || 'Argument') + (typeof n == 'number'
+         ? n < min || n > max ? ' out of range: ' : ' not an integer: '
+         : ' not a primitive number: ') + String(n));
+    }
+  }
+
+
+  // Assumes finite n.
+  function isOdd(n) {
+    var k = n.c.length - 1;
+    return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
+  }
+
+
+  function toExponential(str, e) {
+    return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
+     (e < 0 ? 'e' : 'e+') + e;
+  }
+
+
+  function toFixedPoint(str, e, z) {
+    var len, zs;
+
+    // Negative exponent?
+    if (e < 0) {
+
+      // Prepend zeros.
+      for (zs = z + '.'; ++e; zs += z);
+      str = zs + str;
+
+    // Positive exponent
+    } else {
+      len = str.length;
+
+      // Append zeros.
+      if (++e > len) {
+        for (zs = z, e -= len; --e; zs += z);
+        str += zs;
+      } else if (e < len) {
+        str = str.slice(0, e) + '.' + str.slice(e);
+      }
+    }
+
+    return str;
+  }
+
+
+  // EXPORT
+
+
+  BigNumber = clone();
+  BigNumber['default'] = BigNumber.BigNumber = BigNumber;
+
+  // AMD.
+  if (typeof define == 'function' && define.amd) {
+    define(function () { return BigNumber; });
+
+  // Node.js and other environments that support module.exports.
+  } else if (typeof module != 'undefined' && module.exports) {
+    module.exports = BigNumber;
+
+  // Browser.
+  } else {
+    if (!globalObject) {
+      globalObject = typeof self != 'undefined' && self ? self : window;
+    }
+
+    globalObject.BigNumber = BigNumber;
+  }
+})(this);
+</script>
     <script type="text/javascript">
     // bip39 Valid Mnemonic Generator Javascript App
     /*

From 49a2b1d412302ba082be1dd46dfafde2888928a4 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 12:10:35 -0400
Subject: [PATCH 31/55] Update index.html

---
 index.html | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/index.html b/index.html
index 2da1e6e..641069a 100644
--- a/index.html
+++ b/index.html
@@ -5508,7 +5508,7 @@ <h2>REVERSIBLE: BIP39 Palindromic Mnemonic Tool</h2>
      <p>STEP 1: Select word count:<p>
      <select id="wordLengthPal">
        <option value=12>SELECT 12 Words (128 bits of security)</option>
-       <option value=24>SELECT 24 Words (128 bits of security)</option>
+       <option value=24>SELECT 24 Words (256 bits of security)</option>
      </select>
      <p>OPTIONAL: Insert entropy in the form of a 0x-padded hex string of length 32 (for 12 words) or 64 (for 24 words):</p>
      <input id="entropyPal">

From a6faa6b81774e5fc4a9b46e0972f723f6c339557 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 17:53:28 -0400
Subject: [PATCH 32/55] removed palindromic mnemonic feature from frontend

While the code still exists for the palindromic mnemonic function I removed the html from the front for the purpose of simplifying the interface and focusing on the Hatnotation part.
---
 index.html | 15 ++-------------
 1 file changed, 2 insertions(+), 13 deletions(-)

diff --git a/index.html b/index.html
index 641069a..3d5be54 100644
--- a/index.html
+++ b/index.html
@@ -5504,21 +5504,10 @@ <h2>REGULAR: BIP39 Mnemonic Tool</h2>
      <br>
      <br>
      <div id="output"></div>
-     <h2>REVERSIBLE: BIP39 Palindromic Mnemonic Tool</h2>
-     <p>STEP 1: Select word count:<p>
-     <select id="wordLengthPal">
-       <option value=12>SELECT 12 Words (128 bits of security)</option>
-       <option value=24>SELECT 24 Words (256 bits of security)</option>
-     </select>
-     <p>OPTIONAL: Insert entropy in the form of a 0x-padded hex string of length 32 (for 12 words) or 64 (for 24 words):</p>
-     <input id="entropyPal">
+  
      <br>
      <br>
-     <button onclick="generateBIP39Palindromic()">STEP 2: Click Here to GENERATE Palindromic Mnemonic Words (Reversible Mnemonic will appear below)</button>
-     <button onclick="clearPalindromic()"> Click Here to CLEAR (Will Delete Data)</button>
-     <br>
-     <br>
-     <div id='outputPal'></div>
+    
      <h2>Decode Base64 Entropy </h2>
      <input id="base64entropy">
      <button onclick="Decrypt()"> Get Seed Words</button>

From bf321b28e250a55a86ecc2f0ba4c207e7c9b5b4b Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 18:38:09 -0400
Subject: [PATCH 33/55] Changed input to accept binary instead of hex

Changed line 102: hexer=int(input('enter binary string with '0b' pad'),2)
---
 base64encode_v1_01.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base64encode_v1_01.py b/base64encode_v1_01.py
index 28f7e78..f2e079d 100644
--- a/base64encode_v1_01.py
+++ b/base64encode_v1_01.py
@@ -99,6 +99,6 @@ def base64en(address_hex):   # important never to rename base64en to "base64" wh
     #for one in range(ones):
      #   b64_string = '1' + b64_string
     return b64_string
-hexer=int(input('enter hex with pad'),16)
+hexer=int(input('enter binary string with '0b' pad'),2)
 print(base64en(hexer))
 print("The above is this many char's long: ",len(str((base64en(hexer)))))

From 95e52b585a7ea9d051a7e0bdec06e88bc31c3121 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 18:38:55 -0400
Subject: [PATCH 34/55] renamed to v1_02

to reflect binary input to avoid 0-pad loss found with hex
---
 base64encode_v1_01.py => base64encode_v1_02.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
 rename base64encode_v1_01.py => base64encode_v1_02.py (99%)

diff --git a/base64encode_v1_01.py b/base64encode_v1_02.py
similarity index 99%
rename from base64encode_v1_01.py
rename to base64encode_v1_02.py
index f2e079d..7c6562d 100644
--- a/base64encode_v1_01.py
+++ b/base64encode_v1_02.py
@@ -4,7 +4,7 @@
 import binascii # required
 
 #Author: Steven Hatzakis @2018, Licensed under Apache 2.0
-# Version 1.01
+# Version 1.02
 
 #test binary data string: 0b010010010111011111001110010111011101001110001101001011100010011100011101001110011111001110010111010001001010011101100011001010010100010010011100111001000010000000000001001000
 

From ce6e3dfb86179889e51079397e3746b20c8edf05 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 18:56:06 -0400
Subject: [PATCH 35/55] Updated version + added note about lost leading zeroes

Example test string to decode: `9$B_,4-C$T(W_O;-)B'0N`
Target decoding result: `0b0000101101000101100000100110100010111111100101001110110100111110110101001101010000001100010110100000001010011101101110100000011110`
Actual decoding result in current version: `0b00101101000101100000100110100010111111100101001110110100111110110101001101010000001100010110100000001010011101101110100000011110`
Current behavior: two leading zeroes missing from above string
Solution to consider: add back leading zeroes when length of string output modulo 6 is greater than zero.
Is 22 characters and should decode to 132 bits but only decodes to 130 as two leading zeroes are lost and must be padded back.
---
 base64Decode_v1_01.py => base64Decode_v1_02.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
 rename base64Decode_v1_01.py => base64Decode_v1_02.py (84%)

diff --git a/base64Decode_v1_01.py b/base64Decode_v1_02.py
similarity index 84%
rename from base64Decode_v1_01.py
rename to base64Decode_v1_02.py
index e3bb203..e30c88e 100644
--- a/base64Decode_v1_01.py
+++ b/base64Decode_v1_02.py
@@ -107,7 +107,7 @@ def decodeAsHex(string):
 
 ## test decode string "HELLOWORLD" should return the binary equivalent of hex: 0x44e55562061b54d
 ## test decode string "INVENTEDBYSTEVENHATZAKIS@2018' should return this hex 0x125df39774e34b89c74e7ce5d129d8ca512739080048 as equivalent in binary to this output: 010010010111011111001110010111011101001110001101001011100010011100011101001110011111001110010111010001001010011101100011001010010100010010011100111001000010000000000001001000
-
+## Note/ WARNING: leading zeroes are not retained in the Hatnotated string, therefore, when decoding the test string `9$B_,4-C$T(W_O;-)B'0N` found in the Readme file, two leading zeroes will not appear. Software implementers should pad enough zeroes to math the Hatnotated character lenght (i.e. 22 pasted characters should compute 132 bits, but if only 130 bits show then 2 leading zeroes shoud be padded. 
 ## Note/CONSIDERATION: In version 1.01 to resolve a rendering conflict, the Forward slash `/` and Backslash `\` characters have been swapped out and replaced by the closing curly bracket `}` and opening curly bracket `{` on purpose.
 
 

From fbda1dbe6b1ba90ff128d1abb32ddbebc356cbb7 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 19:03:28 -0400
Subject: [PATCH 36/55] Update README.md

---
 README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index 6cbe302..e72d6e6 100644
--- a/README.md
+++ b/README.md
@@ -13,7 +13,7 @@ An encoding/decoding method that allows users to compress their human-readable d
 
 ## Warning: 
 
-This software is still in its experimental phase (including debugging, redesign and error-checking/testing) and should not be relied upon for production.  
+This software is still in its experimental phase (including debugging, redesign and error-checking/testing) and should not be relied upon for production. For example, as of April 30 before the conclusion of the Ethereal Hackathon our Javascript versions of the Decoder were still being debugged. And while our Python versions were fully functional and working correctly, when encoding a binary string that contains leading padded-zeroes (i.e. empty placeholder values not part of an actual   number but simply indicating a potential range of numbers that the acutal number is within) those zeroes are not mapped and therefore when decoding Hatnotated data that originally contained such numbers, they will be lost (i.e. were lost on encoding and thus are not there when decoding either). There is a workaround for this that is being considered, but the onus is on the user to know such data when initially encoding any aribtrary string. For the sake of mnemonics used in this example the solution is easy, but other cases could be more complex. See this issue for more on leading zeroes: https://github.com/hatgit/hatnotation/issues/6
 
 ## Background on Mnemonics (private keys) and Human vs Machine-readable code
 
@@ -49,6 +49,8 @@ In terms of actual pre-image resistance, the initial entropy should be generated
 
 - >Hatnotation format:
  > `9$B_,4-C$T(W_O;-)B'0N`
+ 
+ NOTE: The above binary string contains two leading zeroes (from a total of four) which are lost during encoding. 
 
 
 ## Important
@@ -171,8 +173,6 @@ In Python version 3.7 using the strings library, the following steps can be take
 
 - And the following four remain excluded/reserved ~~```"\/|~"```~~).
 
-
-
 ## Requirements
 
 Python 3 or higher

From fb76595bc3af807b862c3168d85da24b2e912e95 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 30 Apr 2019 19:14:40 -0400
Subject: [PATCH 37/55] Corrected Test Strings to include checksum

The example notation methods for a given string example was missing its 4-bit checksum at the end of the first binary string which had a waterfall effect on the subsequent examples. All have been fixed now:

### Example of various notation methods for a given binary (base 2) string:

- 132-bit Binary (base-2) format with leading 0b):
>`0b000010011001110010111111101011110001001100000011001001110111011010111000001111100110001101001100001011000010111010100000000101111110`
- 32-character Hexidecimal(base-16) format (with leading 0x):
> `0x99cbfaf13032776b83e634c2c2ea017e`
- 39-decimal (base-10) integer format:
>`204431009328679068125508232041575612798`
- 12-word Mnemonic format (BIP39):
>`another tourist type champion crash robust thought small equip gesture pool cool`  (note: this mnemonic conveys 132 bits as the extra 4-bit checksum '1110' from the above binary string is deterministic based on the initial 128 bits).</ul></li>

- >Hatnotation format:
 > 2P{`(.C39>Q?F#DCB2[W5_
---
 README.md | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/README.md b/README.md
index e72d6e6..719cc86 100644
--- a/README.md
+++ b/README.md
@@ -13,7 +13,7 @@ An encoding/decoding method that allows users to compress their human-readable d
 
 ## Warning: 
 
-This software is still in its experimental phase (including debugging, redesign and error-checking/testing) and should not be relied upon for production. For example, as of April 30 before the conclusion of the Ethereal Hackathon our Javascript versions of the Decoder were still being debugged. And while our Python versions were fully functional and working correctly, when encoding a binary string that contains leading padded-zeroes (i.e. empty placeholder values not part of an actual   number but simply indicating a potential range of numbers that the acutal number is within) those zeroes are not mapped and therefore when decoding Hatnotated data that originally contained such numbers, they will be lost (i.e. were lost on encoding and thus are not there when decoding either). There is a workaround for this that is being considered, but the onus is on the user to know such data when initially encoding any aribtrary string. For the sake of mnemonics used in this example the solution is easy, but other cases could be more complex. See this issue for more on leading zeroes: https://github.com/hatgit/hatnotation/issues/6
+This software is still in its experimental phase (including debugging, redesign and error-checking/testing) and should not be relied upon for production. For example, as of April 30 before the conclusion of the Ethereal Hackathon our Javascript versions of the Decoder were still being debugged. 
 
 ## Background on Mnemonics (private keys) and Human vs Machine-readable code
 
@@ -38,19 +38,19 @@ In terms of actual pre-image resistance, the initial entropy should be generated
 
 ### Example of various notation methods for a given binary (base 2) string: 
 
-- Binary (base-2) format: 
->`00001001100111001011111110101111000100110000001100100111011101101011100000111110011000110100110000101100001011101010000000010111`
-- Hexidecimal(base-16) format: 
-> `99cbfaf13032776b83e634c2c2ea017`
-- Decimal (base-10) integer format: 
->`12776938083042441757844264502598475799`
-- Mnemonic format (BIP39): 
->`another tourist type champion crash robust thought small equip gesture pool cool`  (note: this mnemonic conveys 132 bits as the extra 4-bit checksum is deterministic based on the initial 128 bits).</ul></li>
+- 132-bit Binary (base-2) format with leading 0b): 
+>`0b000010011001110010111111101011110001001100000011001001110111011010111000001111100110001101001100001011000010111010100000000101111110`
+- 32-character Hexidecimal(base-16) format (with leading 0x): 
+> `0x99cbfaf13032776b83e634c2c2ea017e`
+- 39-decimal (base-10) integer format: 
+>`204431009328679068125508232041575612798`
+- 12-word Mnemonic format (BIP39): 
+>`another tourist type champion crash robust thought small equip gesture pool cool`  (note: this mnemonic conveys 132 bits as the extra 4-bit checksum '1110' from the above binary string is deterministic based on the initial 128 bits).</ul></li>
 
 - >Hatnotation format:
- > `9$B_,4-C$T(W_O;-)B'0N`
+ > 2P{`(.C39>Q?F#DCB2[W5_
  
- NOTE: The above binary string contains two leading zeroes (from a total of four) which are lost during encoding. 
+  
 
 
 ## Important

From 704791299a1ab7ef27304146f1b5250f5d0a5bf4 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sun, 9 Jun 2019 11:51:03 -0400
Subject: [PATCH 38/55] corrected missing binary in test string

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 719cc86..ef09d5c 100644
--- a/README.md
+++ b/README.md
@@ -204,7 +204,7 @@ The easiest of this example can be seen using the Hatnotation library of 64 char
 
 The library in binary format as a continous string: 
 
-000000000001000010000011000100000101000110000111001000001001001010001011001100001101001110001111010000010001010010010011010100010101010110010111011000011001011010011011011100011101011110011111100000100001100010100011100100100101100110100111101000101001101010101011101100101110101111110000110001110010110011110100110101110110110111111000111001111010111011111100111101111110111111
+000000000001000010000011000100000101000110000111001000001001001010001011001100001101001110001111010000010001010010010011010100010101010110010111011000011001011010011011011100011101011110011111100000100001100010100011100100100101100110100111101000101001101010101011101100101101101110101111110000110001111011110011110100110101110110110111111000111001111010110010111100111101111110111111
 
 The above 384-bit binary string (based on 64*6 bits) in hex is: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
 

From e24ec91877a7b894830b87fb9b63154722dc172e Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sun, 9 Jun 2019 13:37:30 -0400
Subject: [PATCH 39/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ef09d5c..d973189 100644
--- a/README.md
+++ b/README.md
@@ -208,7 +208,7 @@ The library in binary format as a continous string:
 
 The above 384-bit binary string (based on 64*6 bits) in hex is: 0x108310518720928b30d38f41149351559761969b71d79f8218a39259a7a29aabb2dbafc31ef3d35db7e39eb2f3dfbf
 
-When the above hex string is encoded back to hatnotation it loses the leading zero (or first 6 zeroes of the above binary string) resulting in it missing from the start of the resulting encoded characters: "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.}:;<=>?@[{]^_`"
+When the above hex string is encoded back to hatnotation it loses the leading zero (or first 6 zeroes of the above binary string) resulting in it missing from the start of the resulting encoded characters: "123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-.{:;<=>?@[}]^_`"
 
 The loss of leading zeroes has been discussed in the following issue and is common across other popular notation systems when converting from left-padded binary data: https://github.com/hatgit/hatnotation/issues/6
 

From f8a1bcf24a7d0636d53c38bbe202fd193a4b6e5f Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Sun, 9 Jun 2019 13:39:32 -0400
Subject: [PATCH 40/55] swapped order of opening & closing curly brackets

The order was incorrect, corrected by swapping them.
---
 base64Decode_v1_02.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/base64Decode_v1_02.py b/base64Decode_v1_02.py
index e30c88e..fb5a4d8 100644
--- a/base64Decode_v1_02.py
+++ b/base64Decode_v1_02.py
@@ -67,7 +67,7 @@
 ",",
 "-",
 ".",
-"}",
+"{",
 ":",
 ";",
 "<",
@@ -76,7 +76,7 @@
 "?",
 "@",
 "[",
-"{",
+"}",
 "]",
 "^",
 "_",

From 5f56d83ec4707d74e8df5dad1ac84b4181819ab4 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 1 Jul 2019 18:11:50 +0300
Subject: [PATCH 41/55] Explained leading zeroes from decoder output

---
 README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.md b/README.md
index d973189..37327ad 100644
--- a/README.md
+++ b/README.md
@@ -212,6 +212,8 @@ When the above hex string is encoded back to hatnotation it loses the leading ze
 
 The loss of leading zeroes has been discussed in the following issue and is common across other popular notation systems when converting from left-padded binary data: https://github.com/hatgit/hatnotation/issues/6
 
+On the subject of leading zeroes, it should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0. In other words, if the following 64-bit string 1111111101110110000010000001010100110110010101010010100100100000 was pasted into the Hatnotation encoder(where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left of the string as follows 001111111101110110000010000001010100110110010101010010100100100000 (so that 66 mod 6 = 0) which would only be noticeable when decoding the Hatnotation back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data. This approach is necessary as appending the zeroes instead at the right end would increase the size of the number versus at the front ( ['111111', '110111', '011000', '001000', '000101', '010011', '011001', '010101', '001010', '010010', '0000']) which could lead to errors, compared to the way the program works now where the output is read as a big-endian number where the most significant bit starts at the left and thus any leading zeroes should be dropped : ['001111', '111101', '110110', '000010', '000001', '010100', '110110', '010101', '010010', '100100', '100000'] (especially as the encoder cannot encode the value 0 at the start position in hatnotation which in binary is "000000").
+
 ** There can be some formatting issues in Python which affect how data is printed as noted in this committ: https://github.com/hatgit/hatnotation/commit/66727918cef8a5bdfad21051d52b9c1e483c7fbc
 
 ## Resources: 

From 6b1d60f0cb6fa628b83261451abafcc02d016706 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 1 Jul 2019 18:14:18 +0300
Subject: [PATCH 42/55] Update README.md

---
 README.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 37327ad..11032cb 100644
--- a/README.md
+++ b/README.md
@@ -8,7 +8,7 @@
 </blockquote>
 
 ## Purpose
-An encoding/decoding method that allows users to compress their human-readable data into fewer human-readable characters than other popular notation systems, for any arbitrary underlying machine-readable binary string. 
+An encoding/decoding method that allows users to compress their human-readable data into fewer human-readable characters than other popular notation systems, for any arbitrary underlying machine-readable binary string, using a 6-bit values from the range of 2^6 values. 
 
 
 ## Warning: 
@@ -212,7 +212,9 @@ When the above hex string is encoded back to hatnotation it loses the leading ze
 
 The loss of leading zeroes has been discussed in the following issue and is common across other popular notation systems when converting from left-padded binary data: https://github.com/hatgit/hatnotation/issues/6
 
-On the subject of leading zeroes, it should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0. In other words, if the following 64-bit string 1111111101110110000010000001010100110110010101010010100100100000 was pasted into the Hatnotation encoder(where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left of the string as follows 001111111101110110000010000001010100110110010101010010100100100000 (so that 66 mod 6 = 0) which would only be noticeable when decoding the Hatnotation back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data. This approach is necessary as appending the zeroes instead at the right end would increase the size of the number versus at the front ( ['111111', '110111', '011000', '001000', '000101', '010011', '011001', '010101', '001010', '010010', '0000']) which could lead to errors, compared to the way the program works now where the output is read as a big-endian number where the most significant bit starts at the left and thus any leading zeroes should be dropped : ['001111', '111101', '110110', '000010', '000001', '010100', '110110', '010101', '010010', '100100', '100000'] (especially as the encoder cannot encode the value 0 at the start position in hatnotation which in binary is "000000").
+##On the subject of leading zeroes: it should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0. In other words, if the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder(where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left of the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data.
+
+This approach is necessary as appending the zeroes instead at the right end would increase the size of the number versus at the front ( `['111111', '110111', '011000', '001000', '000101', '010011', '011001', '010101', '001010', '010010', '0000']`) which could lead to errors, compared to the way the program works now where the output is read as a big-endian number where the most significant bit starts at the left and thus any leading zeroes should be dropped : [`'001111', '111101', '110110', '000010', '000001', '010100', '110110', '010101', '010010', '100100', '100000'`] (especially as the encoder cannot encode the value `0` at the start position in hatnotation which in binary is "`000000`").
 
 ** There can be some formatting issues in Python which affect how data is printed as noted in this committ: https://github.com/hatgit/hatnotation/commit/66727918cef8a5bdfad21051d52b9c1e483c7fbc
 

From f2670acfb6f4301c82d56c6641b258db11743c90 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 1 Jul 2019 18:58:40 +0300
Subject: [PATCH 43/55] corrected hex value used in example

the hex string in the example was missing a leading 0.
---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 11032cb..2ae5331 100644
--- a/README.md
+++ b/README.md
@@ -40,8 +40,8 @@ In terms of actual pre-image resistance, the initial entropy should be generated
 
 - 132-bit Binary (base-2) format with leading 0b): 
 >`0b000010011001110010111111101011110001001100000011001001110111011010111000001111100110001101001100001011000010111010100000000101111110`
-- 32-character Hexidecimal(base-16) format (with leading 0x): 
-> `0x99cbfaf13032776b83e634c2c2ea017e`
+- 33-character Hexidecimal(base-16) format (with leading 0x): 
+> `0x099cbfaf13032776b83e634c2c2ea017e`
 - 39-decimal (base-10) integer format: 
 >`204431009328679068125508232041575612798`
 - 12-word Mnemonic format (BIP39): 

From 2c1882d1589e9ac3a6570ffa9a58370fd8a8a544 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 1 Jul 2019 19:59:09 +0300
Subject: [PATCH 44/55] Update README.md

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 2ae5331..5922c49 100644
--- a/README.md
+++ b/README.md
@@ -212,7 +212,8 @@ When the above hex string is encoded back to hatnotation it loses the leading ze
 
 The loss of leading zeroes has been discussed in the following issue and is common across other popular notation systems when converting from left-padded binary data: https://github.com/hatgit/hatnotation/issues/6
 
-##On the subject of leading zeroes: it should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0. In other words, if the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder(where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left of the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data.
+## On the subject of leading zeroes (different note): 
+It should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0. In other words, if the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder(where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left of the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data.
 
 This approach is necessary as appending the zeroes instead at the right end would increase the size of the number versus at the front ( `['111111', '110111', '011000', '001000', '000101', '010011', '011001', '010101', '001010', '010010', '0000']`) which could lead to errors, compared to the way the program works now where the output is read as a big-endian number where the most significant bit starts at the left and thus any leading zeroes should be dropped : [`'001111', '111101', '110110', '000010', '000001', '010100', '110110', '010101', '010010', '100100', '100000'`] (especially as the encoder cannot encode the value `0` at the start position in hatnotation which in binary is "`000000`").
 

From 85c74f2618e3bc07851b052acba3b3c6b7d8f76b Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 6 Aug 2019 12:51:11 +0300
Subject: [PATCH 45/55] Add Note re leading zeroes for various str lengths

**When leading zeroes CAN be discarded:** If the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder (where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left when decoding back into the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation `F^=21K=LI!W` back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data (There is however, an exception to this rule noted below in the next example).

As noted above, the **exception when leading zeroes should NOT be discarded** is when the length of the string being encoded is already equal to zero when modulo 6, and thus leading zeroes are already present such as in the following string, `001111111101110110000010000001010100110110010101010010100100100000` which when encoded whould appear also as `F^=21K=LI!W` and indistinguishable from an indentical string that lacked such two leading zeroes prior to encoding, and thus the user must retain the initial length of the string prior to encoding, in order to decided whether any leading zeroes should be discarded or not when decoding back to the initial data.
---
 README.md | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 5922c49..3fa1e4e 100644
--- a/README.md
+++ b/README.md
@@ -213,7 +213,11 @@ When the above hex string is encoded back to hatnotation it loses the leading ze
 The loss of leading zeroes has been discussed in the following issue and is common across other popular notation systems when converting from left-padded binary data: https://github.com/hatgit/hatnotation/issues/6
 
 ## On the subject of leading zeroes (different note): 
-It should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0. In other words, if the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder(where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left of the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data.
+It should be noted that if the Decoder happens to output a leading zero at the start of the string, any such continous run of zeroes (up to 5) can be discarded and means that the program appended the zero(s) because the length of the encoded binary data modulo 6 was greater than 0, unless the length of data modulo 6 is equal to zero and there are still leading zeroes. 
+
+**When leading zeroes CAN be discarded:** If the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder (where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left when decoding back into the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation `F^=21K=LI!W` back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data (There is however, an exception to this rule noted below in the next example).
+
+As noted above, the **exception when leading zeroes should NOT be discarded** is when the length of the string being encoded is already equal to zero when modulo 6, and thus leading zeroes are already present such as in the following string, `001111111101110110000010000001010100110110010101010010100100100000` which when encoded whould appear also as `F^=21K=LI!W` and indistinguishable from an indentical string that lacked such two leading zeroes prior to encoding, and thus the user must retain the initial length of the string prior to encoding, in order to decided whether any leading zeroes should be discarded or not when decoding back to the initial data. 
 
 This approach is necessary as appending the zeroes instead at the right end would increase the size of the number versus at the front ( `['111111', '110111', '011000', '001000', '000101', '010011', '011001', '010101', '001010', '010010', '0000']`) which could lead to errors, compared to the way the program works now where the output is read as a big-endian number where the most significant bit starts at the left and thus any leading zeroes should be dropped : [`'001111', '111101', '110110', '000010', '000001', '010100', '110110', '010101', '010010', '100100', '100000'`] (especially as the encoder cannot encode the value `0` at the start position in hatnotation which in binary is "`000000`").
 

From e11fc3909434b4a45f8ac5cdfe3d55d319bddf47 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 6 Aug 2019 12:51:51 +0300
Subject: [PATCH 46/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3fa1e4e..4eeb6e3 100644
--- a/README.md
+++ b/README.md
@@ -217,7 +217,7 @@ It should be noted that if the Decoder happens to output a leading zero at the s
 
 **When leading zeroes CAN be discarded:** If the following 64-bit string `1111111101110110000010000001010100110110010101010010100100100000` was pasted into the Hatnotation encoder (where 64 mod 6 = 4), there would be two zeroes automatically appended by the program to the left when decoding back into the string as follows `001111111101110110000010000001010100110110010101010010100100100000` (so that `66 mod 6 = 0`) which would only be noticeable when decoding the Hatnotation `F^=21K=LI!W` back to binary using the decoder, where two leading zeroes would appear and which should be discarded to obtain the original binary data (There is however, an exception to this rule noted below in the next example).
 
-As noted above, the **exception when leading zeroes should NOT be discarded** is when the length of the string being encoded is already equal to zero when modulo 6, and thus leading zeroes are already present such as in the following string, `001111111101110110000010000001010100110110010101010010100100100000` which when encoded whould appear also as `F^=21K=LI!W` and indistinguishable from an indentical string that lacked such two leading zeroes prior to encoding, and thus the user must retain the initial length of the string prior to encoding, in order to decided whether any leading zeroes should be discarded or not when decoding back to the initial data. 
+As noted above, the **exception when leading zeroes should NOT be discarded** is when the length of the string being encoded is already equal to zero when modulo 6, and thus leading zeroes are already present such as in the following string, `001111111101110110000010000001010100110110010101010010100100100000` which when encoded would appear also as `F^=21K=LI!W` and indistinguishable from an identical string that lacked such two leading zeroes prior to encoding, and thus the user must retain the initial length of the string prior to encoding, in order to decide whether any leading zeroes should be discarded or not when decoding back to the initial data. 
 
 This approach is necessary as appending the zeroes instead at the right end would increase the size of the number versus at the front ( `['111111', '110111', '011000', '001000', '000101', '010011', '011001', '010101', '001010', '010010', '0000']`) which could lead to errors, compared to the way the program works now where the output is read as a big-endian number where the most significant bit starts at the left and thus any leading zeroes should be dropped : [`'001111', '111101', '110110', '000010', '000001', '010100', '110110', '010101', '010010', '100100', '100000'`] (especially as the encoder cannot encode the value `0` at the start position in hatnotation which in binary is "`000000`").
 

From 8dc31d453caeb6867ac3341916b7dedddbe38f37 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 6 Aug 2019 14:22:07 +0300
Subject: [PATCH 47/55] Added Hatnotation Password Generator

Author: Steven Hatzakis @ 2019

A cryptographically-secure password generator that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library.
---
 Hatnotation-Password-Generator.py | 114 ++++++++++++++++++++++++++++++
 1 file changed, 114 insertions(+)
 create mode 100644 Hatnotation-Password-Generator.py

diff --git a/Hatnotation-Password-Generator.py b/Hatnotation-Password-Generator.py
new file mode 100644
index 0000000..bd793e6
--- /dev/null
+++ b/Hatnotation-Password-Generator.py
@@ -0,0 +1,114 @@
+import string
+import secrets
+import sys
+import math
+
+Author: Steven Hatzakis @ 2019
+
+A cryptographically-secure password generator that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library.
+
+alphabet = ["0",
+"1",
+"2",
+"3",
+"4",
+"5",
+"6",
+"7",
+"8",
+"9",
+"A",
+"B",
+"C",
+"D",
+"E",
+"F",
+"G",
+"H",
+"I",
+"J",
+"K",
+"L",
+"M",
+"N",
+"O",
+"P",
+"Q",
+"R",
+"S",
+"T",
+"U",
+"V",
+"W",
+"X",
+"Y",
+"Z",
+"!",
+'"',
+"#",
+"$",
+"%",
+"&",
+"'",
+"(",
+")",
+"*",
+'+',
+",",
+"-",
+".",
+"{",
+":",
+";",
+"<",
+"=",
+">",
+"?",
+"@",
+"[",
+"}",
+"]",
+"^",
+"_",
+"`"]
+joinedalphabet="".join(alphabet)
+print('this is the alphabet we will be using:',joinedalphabet, 
+'which has', len(alphabet), 'characters (total 64), and where the length of passwords generated randomly from this alphabet will determine their strength in terms of bits of security (entropy).') 
+print(len(string.ascii_letters + string.digits+ string.punctuation))
+
+password22 = ''.join(secrets.choice(alphabet) for i in range(22))
+password44 = ''.join(secrets.choice(alphabet) for i in range(44))
+password64 = ''.join(secrets.choice(alphabet) for i in range(64))
+password176 = ''.join(secrets.choice(alphabet) for i in range(176))
+
+
+library=64 #used to calculate entropy
+
+numberchars22=len(password22)
+entropy22=library**numberchars22
+logentropy22=math.log2(entropy22)
+print(password22)
+print("your above",len(password22), "character-long password has entropy of security in this many bits",int(logentropy22)) #sys.getsizeof(password20),"bits long")
+
+numberchars44=len(password44)
+entropy44=library**numberchars44
+logentropy44=math.log2(entropy44)
+print(password44)
+print("your above",len(password44), "character-long password has entropy of security in this many bits",int(logentropy44))#sys.getsizeof(password79),"bits long")
+
+
+numberchars64=len(password64)
+entropy64=library**numberchars64
+logentropy64=math.log2(entropy64)
+print(password64)
+print("your above",len(password64), "character-long password has entropy of security in this many bits" ,int(logentropy64))#,sys.getsizeof(password207),"bits long")
+
+numberchars176=len(password176)
+entropy176=library**numberchars176
+logentropy176=math.log2(entropy176)
+print(password176)
+print("your above",len(password176), "character-long password has entropy of security in this many bits" ,int(logentropy176))#,sys.getsizeof(password207),"bits long")
+
+
+print("START Alphabet",alphabet,"END Alphabet")
+

From ec219d29a371385d563e66ab1e2113a8443d025e Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 6 Aug 2019 14:26:50 +0300
Subject: [PATCH 48/55] Update README.md

---
 README.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/README.md b/README.md
index 4eeb6e3..d65a93e 100644
--- a/README.md
+++ b/README.md
@@ -235,3 +235,10 @@ This approach is necessary as appending the zeroes instead at the right end woul
 - potentially propose a request for comments (RFC) for consideration as a standard.
 - add error message for invalid characters (i.e. lowercase and reserved characters `\|/~`
 
+# About Hatnotation-Password-Generator-Python.py
+
+Author: Steven Hatzakis @ 2019
+
+A cryptographcially-secure password generator that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library (i.e. Generates passwords that only use the 64 Hatnotation characters).
+
+

From dfad77f511db8aebd36eb057240dc53ae9fad694 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 6 Aug 2019 14:27:23 +0300
Subject: [PATCH 49/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index d65a93e..d197b75 100644
--- a/README.md
+++ b/README.md
@@ -235,7 +235,7 @@ This approach is necessary as appending the zeroes instead at the right end woul
 - potentially propose a request for comments (RFC) for consideration as a standard.
 - add error message for invalid characters (i.e. lowercase and reserved characters `\|/~`
 
-# About Hatnotation-Password-Generator-Python.py
+# About Hatnotation-Password-Generator.py
 
 Author: Steven Hatzakis @ 2019
 

From dec293114599e9ed5961b0aac3cbe270501f442a Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Tue, 20 Aug 2019 01:59:37 -0400
Subject: [PATCH 50/55] Added comparison to Base64 encoding

- 33-Hex converted to 16 bytes totalling 35 characters excluding backslahes and b-pad:
> b'\x99\xcb\xfa\xf102wk\x83\xe64\xc2\xc2\xea\x01~'

- Base64 totalling 24-characters excluding b-pad:
>`b'mcv68TAyd2uD5jTCwuoBfg=='`
---
 README.md | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index d197b75..65513be 100644
--- a/README.md
+++ b/README.md
@@ -40,15 +40,24 @@ In terms of actual pre-image resistance, the initial entropy should be generated
 
 - 132-bit Binary (base-2) format with leading 0b): 
 >`0b000010011001110010111111101011110001001100000011001001110111011010111000001111100110001101001100001011000010111010100000000101111110`
+
 - 33-character Hexidecimal(base-16) format (with leading 0x): 
 > `0x099cbfaf13032776b83e634c2c2ea017e`
+
+- 16-bytes totalling 35 characters excluding backslahes and b-pad: 
+> b'\x99\xcb\xfa\xf102wk\x83\xe64\xc2\xc2\xea\x01~'
+
+- 24-character Base64 excluding b-pad:
+>`b'mcv68TAyd2uD5jTCwuoBfg=='`
+
 - 39-decimal (base-10) integer format: 
 >`204431009328679068125508232041575612798`
+
 - 12-word Mnemonic format (BIP39): 
 >`another tourist type champion crash robust thought small equip gesture pool cool`  (note: this mnemonic conveys 132 bits as the extra 4-bit checksum '1110' from the above binary string is deterministic based on the initial 128 bits).</ul></li>
 
-- >Hatnotation format:
- > 2P{`(.C39>Q?F#DCB2[W5_
+- 22-character Hatnotation format:
+> 2P{`(.C39>Q?F#DCB2[W5_
  
   
 

From a3ce01ce033ac499b42227b541227eb0fc345258 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Fri, 13 Sep 2019 20:42:49 +0300
Subject: [PATCH 51/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 65513be..b6c6267 100644
--- a/README.md
+++ b/README.md
@@ -248,6 +248,6 @@ This approach is necessary as appending the zeroes instead at the right end woul
 
 Author: Steven Hatzakis @ 2019
 
-A cryptographcially-secure password generator that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library (i.e. Generates passwords that only use the 64 Hatnotation characters).
+A cryptographcially-secure (password generator)[https://github.com/hatgit/hatnotation/blob/master/Hatnotation-Password-Generator.py] that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library (i.e. Generates passwords that only use the 64 Hatnotation characters).
 
 

From 21ae54a9f0b9194f04f5583c011a7dbbb418ea34 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Fri, 13 Sep 2019 20:43:22 +0300
Subject: [PATCH 52/55] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b6c6267..47bc99e 100644
--- a/README.md
+++ b/README.md
@@ -248,6 +248,6 @@ This approach is necessary as appending the zeroes instead at the right end woul
 
 Author: Steven Hatzakis @ 2019
 
-A cryptographcially-secure (password generator)[https://github.com/hatgit/hatnotation/blob/master/Hatnotation-Password-Generator.py] that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library (i.e. Generates passwords that only use the 64 Hatnotation characters).
+A cryptographcially-secure [password generator](https://github.com/hatgit/hatnotation/blob/master/Hatnotation-Password-Generator.py) that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library (i.e. Generates passwords that only use the 64 Hatnotation characters).
 
 

From 5e840ada3e7307a4e1913a4148992e55540770f0 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 16 Dec 2019 01:51:50 -0500
Subject: [PATCH 53/55] Update README.md

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 47bc99e..614e93d 100644
--- a/README.md
+++ b/README.md
@@ -44,10 +44,10 @@ In terms of actual pre-image resistance, the initial entropy should be generated
 - 33-character Hexidecimal(base-16) format (with leading 0x): 
 > `0x099cbfaf13032776b83e634c2c2ea017e`
 
-- 16-bytes totalling 35 characters excluding backslahes and b-pad: 
+- 16-bytes totalling 35 characters excluding backslahes: 
 > b'\x99\xcb\xfa\xf102wk\x83\xe64\xc2\xc2\xea\x01~'
 
-- 24-character Base64 excluding b-pad:
+- 24-character Base64:
 >`b'mcv68TAyd2uD5jTCwuoBfg=='`
 
 - 39-decimal (base-10) integer format: 

From 2eaa49fcc21835d2f6c5a383dfaceb759d8d6b50 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Fri, 14 Aug 2020 09:26:40 +0300
Subject: [PATCH 54/55] Commented out two comment lines.

---
 Hatnotation-Password-Generator.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Hatnotation-Password-Generator.py b/Hatnotation-Password-Generator.py
index bd793e6..ccfaea9 100644
--- a/Hatnotation-Password-Generator.py
+++ b/Hatnotation-Password-Generator.py
@@ -3,9 +3,9 @@
 import sys
 import math
 
-Author: Steven Hatzakis @ 2019
+#Author: Steven Hatzakis @ 2019
 
-A cryptographically-secure password generator that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library.
+#A cryptographically-secure password generator that uses Python's built-in "secrets" module and that is compatible with the Hatnotation library.
 
 alphabet = ["0",
 "1",

From 85c6d87a806285196b2850b7354771487b23c421 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Fri, 14 Aug 2020 09:39:43 +0300
Subject: [PATCH 55/55] User-specifies entropy size / password length

This version of the Hatnotation password generator allows the user to choose the password length and resulting entropy size in bits of security. A 22-character password will have 128 bits of security.
---
 Password_Generator_python-hatnotation_v3.py | 92 +++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 Password_Generator_python-hatnotation_v3.py

diff --git a/Password_Generator_python-hatnotation_v3.py b/Password_Generator_python-hatnotation_v3.py
new file mode 100644
index 0000000..1e54b6b
--- /dev/null
+++ b/Password_Generator_python-hatnotation_v3.py
@@ -0,0 +1,92 @@
+import string
+import secrets
+import sys
+import math
+
+#Author:  © Steven J Hatzakis, 2020
+
+alphabet = ["0",
+"1",
+"2",
+"3",
+"4",
+"5",
+"6",
+"7",
+"8",
+"9",
+"A",
+"B",
+"C",
+"D",
+"E",
+"F",
+"G",
+"H",
+"I",
+"J",
+"K",
+"L",
+"M",
+"N",
+"O",
+"P",
+"Q",
+"R",
+"S",
+"T",
+"U",
+"V",
+"W",
+"X",
+"Y",
+"Z",
+"!",
+'"',
+"#",
+"$",
+"%",
+"&",
+"'",
+"(",
+")",
+"*",
+'+',
+",",
+"-",
+".",
+"{",
+":",
+";",
+"<",
+"=",
+">",
+"?",
+"@",
+"[",
+"}",
+"]",
+"^",
+"_",
+"`"]
+joinedalphabet="".join(alphabet)
+print('This is the alphabet we will be using:',joinedalphabet, 'which has', len(alphabet), 'characters (total 64), and where the length of passwords generated randomly from this alphabet will determine their strength in terms of bits of security (entropy).') 
+print(len(string.ascii_letters + string.digits+ string.punctuation))
+
+# total printable is 95 with whitespace:
+#'0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ!"#$%&'()*+,-./:;<=>?@[\]^_`{|}~ '
+char=int(input('Please enter a number (i.e. enter ''22'' for a 22-character password with 128 bits of security):'))
+password = ''.join(secrets.choice(alphabet) for i in range(char))
+
+library=64 #used to calculate entropy
+
+numberchars=len(password)
+entropy=library**numberchars
+logentropy=math.log2(entropy)
+print(password)
+print("your above",len(password),
+      "character-long password has entropy of security in this many bits",
+      int(logentropy))
+
+
+