SECCON 2016 Online CTF - Binary/Crypto500 Obfuscated AES Write up (English)



Hello, I'm h2spice working at the LINE Corporation As a security engineer.
This is write-up for SECCON2016 Online CTF-Binary / Crypto500 Obfuscated AES.
This year, unlike last year, I focused on several Mitigation Techniques as software protection method, rather than focusing on exploitation for vulnerabilities in service.


I implemented a white-box AES and applied LLVM obfuscation.

I personally expected to be solved in a variety of ways, but only one team got the flag unlike what I expected.
I thank to PPP 😊
If there was more time, I think all the players could get the flag.
You can download the APK from the link below. Please feel free to contact me if you have any questions.
OAES.zip [Download]

I think there are many ways to solve without knowledge for the white-box AES,
My write-up is genuinely targeting Chow et al. 's white-box AES scheme.
(https://www.cs.colorado.edu/~jrblack/class/csci7000/s03/project/oorschot-whitebox.pdf)

OAES is a simple Android Application that prints an encrypted Flag.
You can get the Flag by finding the hidden secretKey in the application and decrypting the encryptedFlag.

You can get the following code by decompiling .apk.

The execution flow is as follows.
  1. There is value that generated between 0 and 3600 and it is used as the index.
  2. The value of table[index] defined in array.xml is stored in encryptedFlag.
    (e.g.,
              <?xml version="1.0" encoding="utf-8"?>
              <resources>
                  <string-array name="tables">
                      <item>g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc=</item>
                      <item>T6i4c4TH+b1yQGKaMdkyzeCErYVHVxtsY1Zw45MJzjM=</item>
                      <item>hPhT8kZaCwlrtgo6Fq6t2e8PuIaQUxoMbqRP0n8nZ14=</item>
                      <item>uGI3zyZ6PrP9ouZg7kp4Gc4rexZxssoYxk9geUeIs54=</item>
                      ....
    The encryptedFlag(item) defined in array.xml is ciphertext that encrypted N(index+1)times with the same secretKey.
  3. print encryptedFlag.
  4. EncryptedFlag is encrypted in the function.a (encryption function) of native-lib.so.
  5. Repeat steps 3 and 4.

Pseudo code (IDA Hex-Rays Decompiler) in Native Function.a is shown below.
int __cdecl Java_kr_repo_h2spice_crypto500_MainActivity_a(int a1, int a2, int input)
{
  // [COLLAPSED LOCAL DECLARATIONS. PRESS KEYPAD CTRL-"+" TO EXPAND]
  v31 = *MK_FP(__GS__, 20);
  input_base64 = (*(*a1 + 676))(a1, input, 0);
  *output_base64_16 = 0LL;
  *output_base64_0 = 0LL;
  v30 = 0;
  DENCPKY6hzMem3SuzgIXu4u6vxbF1sajPOJ75aN2VTdc7SCL(output_base64, input_base64);
  // base64Decode
  *cipherText_16 = 0LL;
  *cipherText_0 = 0LL;
  TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq(output_base64, cipherText);
  // encryption 16bytes
  TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq(output_base64+16, cipherText+16);
  // encryption 16bytes
  
  *base64_out_final = 0LL;
  APtMDGO79Go3cbIkFca2rN0KszanZXOZ7dIPsxDBletW5gdo(base64_out_final, cipherText, 32);// base64Encode
  ...

The execution flow is as follows.
  1. The data (base64 encoded) received from Java is base64 decoded.
    (base64decode funciton : DENCPKY6hzMem3SuzgIXu4u6vxbF1sajPOJ75aN2VTdc7SCL)
  2. Encrypt per one block(16bytes) at a time.
    (encryption function : TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq)
  3. Encrypted data (32bytes) is base64 encoded.
    (base64encode function : APtMDGO79Go3cbIkFca2rN0KszanZXOZ7dIPsxDBletW5gdo)
You need to analyze the encryption function (TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq) and find the secret-key used for encryption.
But it is obfuscated and it is tricky. (But I think it is an obfuscation that can be analyzed sufficiently.)


Theoretically, I will briefly explain the white-box AES implemented in OAES.
Of course, there are many ways to solve without the knowledge of the white-box AES.

Conventional AES Scheme can be transformed into the following form.
  1. The for-loop can be redefined to bring the transformation AddRoundKey(state, k0) inside it while pushing AddRoundKey(state, k9) out.
  2. Since SubBytes applies the same S-box to each byte of the state, SubBytes followed by ShiftRows gives the same result as ShiftRows followed by SubBytes.
  3. Since ShiftRows is a linear transformation (recall that it is a permutation),AddRoundKey(state, kr−1) followed by ShiftRows(state) gives the same result as ShiftRows(state) followed by AddRoundKey(state, ḱr−1); here, ḱr−1 is the result of applying ShiftRows to the round key kr−1.
Chow et al.'s White-box AES Scheme is based on Table (T-boxes) basically. And AddRoundKey, SubBytes transformation can be combined. e.g., SubBytes(AddRoundKey(state,kr))
Each round operation can be composed as a pre-computed LUT and plaintext can be encrypted based on T-boxes.

T-boxes are created with the following formula.

In other words, T-box of Round1 can be created as follows.



char TboxesRound1[16][256] = 
{       
    /*Round0 ḱ[0] is 0x6c*/
    {
        0x50, 0x3c, 0x9f, 0xa8, 0x45, 0xf9, 0x02, 0x7f, 0x43, 0x4d, 0x33, 0x85, 0xd0, 0xef, 0xaa, 0xfb,
        0x10, 0xff, 0xf3, 0xd2, 0xbc, 0xb6, 0xda, 0x21, 0x92, 0x9d, 0x38, 0xf5, 0x51, 0xa3, 0x40, 0x8f,
        0x29, 0xe3, 0x2f, 0x84, 0x52, 0x3b, 0xd6, 0xb3, 0x1b, 0x6e, 0x5a, 0xa0, 0x09, 0x83, 0x2c, 0x1a,
        0x4a, 0x4c, 0x58, 0xcf, 0x6a, 0xcb, 0xbe, 0x39, 0x20, 0xfc, 0xb1, 0x5b, 0x53, 0xd1, 0x00, 0xed,
        0x71, 0xd8, 0x31, 0x15, 0x34, 0xa5, 0xe5, 0xf1, 0x36, 0x3f, 0xf7, 0xcc, 0xb7, 0xfd, 0x93, 0x26,
        0xeb, 0x27, 0xb2, 0x75, 0x07, 0x12, 0x80, 0xe2, 0x18, 0x96, 0x05, 0x9a, 0x04, 0xc7, 0x23, 0xc3,
        0xfe, 0xd7, 0xab, 0x76, 0x30, 0x01, 0x67, 0x2b, 0xf2, 0x6b, 0x6f, 0xc5, 0x63, 0x7c, 0x77, 0x7b,
        0x9c, 0xa4, 0x72, 0xc0, 0xad, 0xd4, 0xa2, 0xaf, 0xfa, 0x59, 0x47, 0xf0, 0xca, 0x82, 0xc9, 0x7d,
        0xce, 0x55, 0x28, 0xdf, 0x9b, 0x1e, 0x87, 0xe9, 0x69, 0xd9, 0x8e, 0x94, 0xe1, 0xf8, 0x98, 0x11,
        0xb0, 0x54, 0xbb, 0x16, 0x41, 0x99, 0x2d, 0x0f, 0xbf, 0xe6, 0x42, 0x68, 0x8c, 0xa1, 0x89, 0x0d,
        0x4b, 0xbd, 0x8b, 0x8a, 0xe8, 0xdd, 0x74, 0x1f, 0x1c, 0xa6, 0xb4, 0xc6, 0xba, 0x78, 0x25, 0x2e,
        0x86, 0xc1, 0x1d, 0x9e, 0x61, 0x35, 0x57, 0xb9, 0x48, 0x03, 0xf6, 0x0e, 0x70, 0x3e, 0xb5, 0x66,
        0x91, 0x95, 0xe4, 0x79, 0xc2, 0xd3, 0xac, 0x62, 0x49, 0x06, 0x24, 0x5c, 0xe0, 0x32, 0x3a, 0x0a,
        0x65, 0x7a, 0xae, 0x08, 0x6c, 0x56, 0xf4, 0xea, 0x8d, 0xd5, 0x4e, 0xa9, 0xe7, 0xc8, 0x37, 0x6d,
        0x64, 0x5d, 0x19, 0x73, 0xc4, 0xa7, 0x7e, 0x3d, 0x5f, 0x97, 0x44, 0x17, 0xcd, 0x0c, 0x13, 0xec,
        0xde, 0x5e, 0x0b, 0xdb, 0x46, 0xee, 0xb8, 0x14, 0x22, 0x2a, 0x90, 0x88, 0x60, 0x81, 0x4f, 0xdc
    },
    /*Round0 ḱ[1] is 0x61*/
    {
        0xef, 0xd0, 0xfb, 0xaa, 0x4d, 0x43, 0x85, 0x33, 0xf9, 0x45, 0x7f, 0x02, 0x3c, 0x50, 0xa8, 0x9f,
        0xa3, 0x51, 0x8f, 0x40, 0x9d, 0x92, 0xf5, 0x38, 0xb6, 0xbc, 0x21, 0xda, 0xff, 0x10, 0xd2, 0xf3,
        0x83, 0x09, 0x1a, 0x2c, 0x6e, 0x1b, 0xa0, 0x5a, 0x3b, 0x52, 0xb3, 0xd6, 0xe3, 0x29, 0x84, 0x2f,
        0xd1, 0x53, 0xed, 0x00, 0xfc, 0x20, 0x5b, 0xb1, 0xcb, 0x6a, 0x39, 0xbe, 0x4c, 0x4a, 0xcf, 0x58,
        0xfd, 0xb7, 0x26, 0x93, 0x3f, 0x36, 0xcc, 0xf7, 0xa5, 0x34, 0xf1, 0xe5, 0xd8, 0x71, 0x15, 0x31,
        0xc7, 0x04, 0xc3, 0x23, 0x96, 0x18, 0x9a, 0x05, 0x12, 0x07, 0xe2, 0x80, 0x27, 0xeb, 0x75, 0xb2,
        0x7c, 0x63, 0x7b, 0x77, 0x6b, 0xf2, 0xc5, 0x6f, 0x01, 0x30, 0x2b, 0x67, 0xd7, 0xfe, 0x76, 0xab,
        0x82, 0xca, 0x7d, 0xc9, 0x59, 0xfa, 0xf0, 0x47, 0xd4, 0xad, 0xaf, 0xa2, 0xa4, 0x9c, 0xc0, 0x72,
        0xf8, 0xe1, 0x11, 0x98, 0xd9, 0x69, 0x94, 0x8e, 0x1e, 0x9b, 0xe9, 0x87, 0x55, 0xce, 0xdf, 0x28,
        0xa1, 0x8c, 0x0d, 0x89, 0xe6, 0xbf, 0x68, 0x42, 0x99, 0x41, 0x0f, 0x2d, 0x54, 0xb0, 0x16, 0xbb,
        0x78, 0xba, 0x2e, 0x25, 0xa6, 0x1c, 0xc6, 0xb4, 0xdd, 0xe8, 0x1f, 0x74, 0xbd, 0x4b, 0x8a, 0x8b,
        0x3e, 0x70, 0x66, 0xb5, 0x03, 0x48, 0x0e, 0xf6, 0x35, 0x61, 0xb9, 0x57, 0xc1, 0x86, 0x9e, 0x1d,
        0x32, 0xe0, 0x0a, 0x3a, 0x06, 0x49, 0x5c, 0x24, 0xd3, 0xc2, 0x62, 0xac, 0x95, 0x91, 0x79, 0xe4,
        0xc8, 0xe7, 0x6d, 0x37, 0xd5, 0x8d, 0xa9, 0x4e, 0x56, 0x6c, 0xea, 0xf4, 0x7a, 0x65, 0x08, 0xae,
        0x0c, 0xcd, 0xec, 0x13, 0x97, 0x5f, 0x17, 0x44, 0xa7, 0xc4, 0x3d, 0x7e, 0x5d, 0x64, 0x73, 0x19,
        0x81, 0x60, 0xdc, 0x4f, 0x2a, 0x22, 0x88, 0x90, 0xee, 0x46, 0x14, 0xb8, 0x5e, 0xde, 0xdb, 0x0b
    },
...

The encryption process using T-boxes is as follows.

MixColumns in each Round can also be composed with four pre-computed LUTs (M0, M1, M2, M3) and can be combined with T-boxes.

Note that state in MixColumns is multiplied in Rijndael's Galois Field, but normal multiplication.


T-boxes + M-boxes (M_T-Boxes) can be composed as follows.
unsigned int M_T-boxesRound1[16][256] =
{   
    /*Round0 ḱ[0] is 0x6c*/
    {
        0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0xcf45458a, 0x10f9f9e9, 0x06020204, 0x817f7ffe, 0xc5434386, 0xd74d4d9a, 0x55333366, 0x94858511, 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed,
        0x30101020, 0x1affffe5, 0x0ef3f3fd, 0x6dd2d2bf, 0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x04f5f5f1, 0xf35151a2, 0xfea3a35d, 0xc0404080, 0x8a8f8f05,
        0x7b292952, 0x3ee3e3dd, 0x712f2f5e, 0x97848413, 0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b, 0x1b090912, 0x9e83831d, 0x742c2c58, 0x2e1a1a34,
        0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, 0xbe6a6ad4, 0x46cbcb8d, 0xd9bebe67, 0x4b393972, 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6, 0xf55353a6, 0x68d1d1b9, 0x00000000, 0x2cededc1,
        0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, 0x5c343468, 0xf4a5a551, 0x34e5e5d1, 0x08f1f1f9, 0x5a36366c, 0x413f3f7e, 0x02f7f7f5, 0x4fcccc83, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c,
        0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x0907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, 0x28181830, 0xa1969637, 0x0f05050a, 0xb59a9a2f, 0x0c040408, 0x52c7c795, 0x65232346, 0x5ec3c39d,
        0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0x50303060, 0x03010102, 0xa96767ce, 0x7d2b2b56, 0x0df2f2ff, 0xbd6b6bd6, 0xb16f6fde, 0x54c5c591, 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6,
        0xbf9c9c23, 0xf7a4a453, 0x967272e4, 0x5bc0c09b, 0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0x0bf0f0fb, 0x45caca8f, 0x9d82821f, 0x40c9c989, 0x877d7dfa,
        0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, 0xb69b9b2d, 0x221e1e3c, 0x92878715, 0x20e9e9c9, 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122,
        0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c, 0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, 0xdabfbf65, 0x31e6e6d7, 0xc6424284, 0xb86868d0, 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a,
        0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, 0x241c1c38, 0xf1a6a657, 0xc7b4b473, 0x51c6c697, 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c,
        0x91868617, 0x58c1c199, 0x271d1d3a, 0xb99e9e27, 0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0xd8484890, 0x05030306, 0x01f6f6f7, 0x120e0e1c, 0x907070e0, 0x423e3e7c, 0xc4b5b571, 0xaa6666cc,
        0xa8919139, 0xa4959531, 0x37e4e4d3, 0x8b7979f2, 0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xdb494992, 0x0a06060c, 0x6c242448, 0xe45c5cb8, 0x3be0e0db, 0x56323264, 0x4e3a3a74, 0x1e0a0a14,
        0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, 0xb46c6cd8, 0xfa5656ac, 0x07f4f4f3, 0x25eaeacf, 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda,
        0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, 0x57c4c493, 0xf2a7a755, 0x827e7efc, 0x473d3d7a, 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3,
        0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, 0x66222244, 0x7e2a2a54, 0xab90903b, 0x8388880b, 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3
    },
    ...

you can see that it is executed in the following flow by analyzing the encryption function, TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq(unsigned __int8 *in, unsigned __int8 *out)

1. ShiftRows, lrsFdMdlAT0vSMVedxmqOkCBF7sCTbhCjYEp1rLP8vatWEGD( )

2. encryption process based on M_T-boxes(SubByte, AddRoundKey, MixColumns)

  • Encrypt data with M-T-boxes

     The M_T-Boxes in the binary are shown below.



4. ShiftRows before last round

5. The last round encryption process based on T-boxes(SubByte, AddRoundKey)

    The T-box of round10 in the binary are shown below.


To decrypt the encryptedFlag "g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc=", you first need to recover the secretKey.

M-boxes, pre-computed MixColumns LUT is independent from the ḱ1...16.
Therefore you can make M-boxes without ḱ1...16 information.

Since the Round1 LUT of M_T-boxes is depended on ḱ1...16, secretKey can also be recovered if T-boxes could be separated from M-T-boxes.

As you can see in the formula below, if x is 0(M_T-boxes1...16[0]), the ḱ1...16  itself becomes index.


Therefore, the secretKey can be obtained by the following steps.
  1. Find the M_T-boxes of Round1.
  2. Create M-boxes.
  3. Create Sbox (0... 255) and use it as index.
    Since S(ḱ0[0...15]) is the index of M-boxes
  4. Get values from M-boxes [index].
  5. Get LUT from M_T-box[j][0] of round1.  j=1...15 (ḱ0[1...15])
  6. Compare the M-boxes [index] and M_T-boxes [j] [0] of Step 4. If the two values are the same, the index becomes ḱ0[j].
  7. Since ḱ is the result of ShiftRows of roundKey0(secretKey), we can obtain secretKey by un-ShiftRows.
The exploit code is as follows.
#!/usr/bin/python
# -*- coding: utf-8 -*-

import base64
from Crypto.Cipher import AES
import binascii

encFlag = "g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc="
print "encryptedFlag:"+ encFlag

Sbox = [
    0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76,
    0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0,
    0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15,
    0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75,
    0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84,
    0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF,
    0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8,
    0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2,
    0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73,
    0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB,
    0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79,
    0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08,
    0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A,
    0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E,
    0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF,
    0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16,
]

matrix_4x4 = [
 1, 2, 0, 0,
 0, 1, 2, 0,
 0, 0, 1, 2,
 2, 0, 0, 1
]

gmul = [
 [ 
  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F, 
  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1A, 0x1B, 0x1C, 0x1D, 0x1E, 0x1F, 
  0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2A, 0x2B, 0x2C, 0x2D, 0x2E, 0x2F, 
  0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3A, 0x3B, 0x3C, 0x3D, 0x3E, 0x3F, 
  0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4A, 0x4B, 0x4C, 0x4D, 0x4E, 0x4F, 
  0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5A, 0x5B, 0x5C, 0x5D, 0x5E, 0x5F, 
  0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6A, 0x6B, 0x6C, 0x6D, 0x6E, 0x6F, 
  0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7A, 0x7B, 0x7C, 0x7D, 0x7E, 0x7F, 
  0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8A, 0x8B, 0x8C, 0x8D, 0x8E, 0x8F, 
  0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9A, 0x9B, 0x9C, 0x9D, 0x9E, 0x9F, 
  0xA0, 0xA1, 0xA2, 0xA3, 0xA4, 0xA5, 0xA6, 0xA7, 0xA8, 0xA9, 0xAA, 0xAB, 0xAC, 0xAD, 0xAE, 0xAF, 
  0xB0, 0xB1, 0xB2, 0xB3, 0xB4, 0xB5, 0xB6, 0xB7, 0xB8, 0xB9, 0xBA, 0xBB, 0xBC, 0xBD, 0xBE, 0xBF, 
  0xC0, 0xC1, 0xC2, 0xC3, 0xC4, 0xC5, 0xC6, 0xC7, 0xC8, 0xC9, 0xCA, 0xCB, 0xCC, 0xCD, 0xCE, 0xCF, 
  0xD0, 0xD1, 0xD2, 0xD3, 0xD4, 0xD5, 0xD6, 0xD7, 0xD8, 0xD9, 0xDA, 0xDB, 0xDC, 0xDD, 0xDE, 0xDF, 
  0xE0, 0xE1, 0xE2, 0xE3, 0xE4, 0xE5, 0xE6, 0xE7, 0xE8, 0xE9, 0xEA, 0xEB, 0xEC, 0xED, 0xEE, 0xEF, 
  0xF0, 0xF1, 0xF2, 0xF3, 0xF4, 0xF5, 0xF6, 0xF7, 0xF8, 0xF9, 0xFA, 0xFB, 0xFC, 0xFD, 0xFE, 0xFF 
 ],
 [ 
  0x00, 0x02, 0x04, 0x06, 0x08, 0x0A, 0x0C, 0x0E, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1A, 0x1C, 0x1E, 
  0x20, 0x22, 0x24, 0x26, 0x28, 0x2A, 0x2C, 0x2E, 0x30, 0x32, 0x34, 0x36, 0x38, 0x3A, 0x3C, 0x3E, 
  0x40, 0x42, 0x44, 0x46, 0x48, 0x4A, 0x4C, 0x4E, 0x50, 0x52, 0x54, 0x56, 0x58, 0x5A, 0x5C, 0x5E, 
  0x60, 0x62, 0x64, 0x66, 0x68, 0x6A, 0x6C, 0x6E, 0x70, 0x72, 0x74, 0x76, 0x78, 0x7A, 0x7C, 0x7E, 
  0x80, 0x82, 0x84, 0x86, 0x88, 0x8A, 0x8C, 0x8E, 0x90, 0x92, 0x94, 0x96, 0x98, 0x9A, 0x9C, 0x9E, 
  0xA0, 0xA2, 0xA4, 0xA6, 0xA8, 0xAA, 0xAC, 0xAE, 0xB0, 0xB2, 0xB4, 0xB6, 0xB8, 0xBA, 0xBC, 0xBE, 
  0xC0, 0xC2, 0xC4, 0xC6, 0xC8, 0xCA, 0xCC, 0xCE, 0xD0, 0xD2, 0xD4, 0xD6, 0xD8, 0xDA, 0xDC, 0xDE, 
  0xE0, 0xE2, 0xE4, 0xE6, 0xE8, 0xEA, 0xEC, 0xEE, 0xF0, 0xF2, 0xF4, 0xF6, 0xF8, 0xFA, 0xFC, 0xFE, 
  0x1B, 0x19, 0x1F, 0x1D, 0x13, 0x11, 0x17, 0x15, 0x0B, 0x09, 0x0F, 0x0D, 0x03, 0x01, 0x07, 0x05, 
  0x3B, 0x39, 0x3F, 0x3D, 0x33, 0x31, 0x37, 0x35, 0x2B, 0x29, 0x2F, 0x2D, 0x23, 0x21, 0x27, 0x25, 
  0x5B, 0x59, 0x5F, 0x5D, 0x53, 0x51, 0x57, 0x55, 0x4B, 0x49, 0x4F, 0x4D, 0x43, 0x41, 0x47, 0x45, 
  0x7B, 0x79, 0x7F, 0x7D, 0x73, 0x71, 0x77, 0x75, 0x6B, 0x69, 0x6F, 0x6D, 0x63, 0x61, 0x67, 0x65, 
  0x9B, 0x99, 0x9F, 0x9D, 0x93, 0x91, 0x97, 0x95, 0x8B, 0x89, 0x8F, 0x8D, 0x83, 0x81, 0x87, 0x85, 
  0xBB, 0xB9, 0xBF, 0xBD, 0xB3, 0xB1, 0xB7, 0xB5, 0xAB, 0xA9, 0xAF, 0xAD, 0xA3, 0xA1, 0xA7, 0xA5, 
  0xDB, 0xD9, 0xDF, 0xDD, 0xD3, 0xD1, 0xD7, 0xD5, 0xCB, 0xC9, 0xCF, 0xCD, 0xC3, 0xC1, 0xC7, 0xC5,
  0xFB, 0xF9, 0xFF, 0xFD, 0xF3, 0xF1, 0xF7, 0xF5, 0xEB, 0xE9, 0xEF, 0xED, 0xE3, 0xE1, 0xE7, 0xE5 
 ],
 [ 
  0x00, 0x03, 0x06, 0x05, 0x0C, 0x0F, 0x0A, 0x09, 0x18, 0x1B, 0x1E, 0x1D, 0x14, 0x17, 0x12, 0x11, 
  0x30, 0x33, 0x36, 0x35, 0x3C, 0x3F, 0x3A, 0x39, 0x28, 0x2B, 0x2E, 0x2D, 0x24, 0x27, 0x22, 0x21, 
  0x60, 0x63, 0x66, 0x65, 0x6C, 0x6F, 0x6A, 0x69, 0x78, 0x7B, 0x7E, 0x7D, 0x74, 0x77, 0x72, 0x71, 
  0x50, 0x53, 0x56, 0x55, 0x5C, 0x5F, 0x5A, 0x59, 0x48, 0x4B, 0x4E, 0x4D, 0x44, 0x47, 0x42, 0x41, 
  0xC0, 0xC3, 0xC6, 0xC5, 0xCC, 0xCF, 0xCA, 0xC9, 0xD8, 0xDB, 0xDE, 0xDD, 0xD4, 0xD7, 0xD2, 0xD1, 
  0xF0, 0xF3, 0xF6, 0xF5, 0xFC, 0xFF, 0xFA, 0xF9, 0xE8, 0xEB, 0xEE, 0xED, 0xE4, 0xE7, 0xE2, 0xE1, 
  0xA0, 0xA3, 0xA6, 0xA5, 0xAC, 0xAF, 0xAA, 0xA9, 0xB8, 0xBB, 0xBE, 0xBD, 0xB4, 0xB7, 0xB2, 0xB1, 
  0x90, 0x93, 0x96, 0x95, 0x9C, 0x9F, 0x9A, 0x99, 0x88, 0x8B, 0x8E, 0x8D, 0x84, 0x87, 0x82, 0x81, 
  0x9B, 0x98, 0x9D, 0x9E, 0x97, 0x94, 0x91, 0x92, 0x83, 0x80, 0x85, 0x86, 0x8F, 0x8C, 0x89, 0x8A, 
  0xAB, 0xA8, 0xAD, 0xAE, 0xA7, 0xA4, 0xA1, 0xA2, 0xB3, 0xB0, 0xB5, 0xB6, 0xBF, 0xBC, 0xB9, 0xBA, 
  0xFB, 0xF8, 0xFD, 0xFE, 0xF7, 0xF4, 0xF1, 0xF2, 0xE3, 0xE0, 0xE5, 0xE6, 0xEF, 0xEC, 0xE9, 0xEA, 
  0xCB, 0xC8, 0xCD, 0xCE, 0xC7, 0xC4, 0xC1, 0xC2, 0xD3, 0xD0, 0xD5, 0xD6, 0xDF, 0xDC, 0xD9, 0xDA, 
  0x5B, 0x58, 0x5D, 0x5E, 0x57, 0x54, 0x51, 0x52, 0x43, 0x40, 0x45, 0x46, 0x4F, 0x4C, 0x49, 0x4A, 
  0x6B, 0x68, 0x6D, 0x6E, 0x67, 0x64, 0x61, 0x62, 0x73, 0x70, 0x75, 0x76, 0x7F, 0x7C, 0x79, 0x7A, 
  0x3B, 0x38, 0x3D, 0x3E, 0x37, 0x34, 0x31, 0x32, 0x23, 0x20, 0x25, 0x26, 0x2F, 0x2C, 0x29, 0x2A, 
  0x0B, 0x08, 0x0D, 0x0E, 0x07, 0x04, 0x01, 0x02, 0x13, 0x10, 0x15, 0x16, 0x1F, 0x1C, 0x19, 0x1A 
 ]
];

M_TBoxesR0 = [
 [
     0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0xcf45458a, 0x10f9f9e9, 0x06020204, 0x817f7ffe, 0xc5434386, 0xd74d4d9a, 0x55333366, 0x94858511, 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed,
     0x30101020, 0x1affffe5, 0x0ef3f3fd, 0x6dd2d2bf, 0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x04f5f5f1, 0xf35151a2, 0xfea3a35d, 0xc0404080, 0x8a8f8f05,
     0x7b292952, 0x3ee3e3dd, 0x712f2f5e, 0x97848413, 0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b, 0x1b090912, 0x9e83831d, 0x742c2c58, 0x2e1a1a34,
     0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, 0xbe6a6ad4, 0x46cbcb8d, 0xd9bebe67, 0x4b393972, 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6, 0xf55353a6, 0x68d1d1b9, 0x00000000, 0x2cededc1,
     0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, 0x5c343468, 0xf4a5a551, 0x34e5e5d1, 0x08f1f1f9, 0x5a36366c, 0x413f3f7e, 0x02f7f7f5, 0x4fcccc83, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c,
     0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x0907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, 0x28181830, 0xa1969637, 0x0f05050a, 0xb59a9a2f, 0x0c040408, 0x52c7c795, 0x65232346, 0x5ec3c39d,
     0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0x50303060, 0x03010102, 0xa96767ce, 0x7d2b2b56, 0x0df2f2ff, 0xbd6b6bd6, 0xb16f6fde, 0x54c5c591, 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6,
     0xbf9c9c23, 0xf7a4a453, 0x967272e4, 0x5bc0c09b, 0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0x0bf0f0fb, 0x45caca8f, 0x9d82821f, 0x40c9c989, 0x877d7dfa,
     0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, 0xb69b9b2d, 0x221e1e3c, 0x92878715, 0x20e9e9c9, 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122,
     0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c, 0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, 0xdabfbf65, 0x31e6e6d7, 0xc6424284, 0xb86868d0, 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a,
     0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, 0x241c1c38, 0xf1a6a657, 0xc7b4b473, 0x51c6c697, 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c,
     0x91868617, 0x58c1c199, 0x271d1d3a, 0xb99e9e27, 0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0xd8484890, 0x05030306, 0x01f6f6f7, 0x120e0e1c, 0x907070e0, 0x423e3e7c, 0xc4b5b571, 0xaa6666cc,
     0xa8919139, 0xa4959531, 0x37e4e4d3, 0x8b7979f2, 0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xdb494992, 0x0a06060c, 0x6c242448, 0xe45c5cb8, 0x3be0e0db, 0x56323264, 0x4e3a3a74, 0x1e0a0a14,
     0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, 0xb46c6cd8, 0xfa5656ac, 0x07f4f4f3, 0x25eaeacf, 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda,
     0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, 0x57c4c493, 0xf2a7a755, 0x827e7efc, 0x473d3d7a, 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3,
     0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, 0x66222244, 0x7e2a2a54, 0xab90903b, 0x8388880b, 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3
 ],
 [
     0xefefc52a, 0xd0d0bb6b, 0xfbfbed16, 0xaaaa4fe5, 0x4d4d9ad7, 0x434386c5, 0x85851194, 0x33336655, 0xf9f9e910, 0x45458acf, 0x7f7ffe81, 0x02020406, 0x3c3c7844, 0x5050a0f0, 0xa8a84be3, 0x9f9f25ba,
     0xa3a35dfe, 0x5151a2f3, 0x8f8f058a, 0x404080c0, 0x9d9d21bc, 0x92923fad, 0xf5f5f104, 0x38387048, 0xb6b677c1, 0xbcbc63df, 0x21214263, 0xdadaaf75, 0xffffe51a, 0x10102030, 0xd2d2bf6d, 0xf3f3fd0e,
     0x83831d9e, 0x0909121b, 0x1a1a342e, 0x2c2c5874, 0x6e6edcb2, 0x1b1b362d, 0xa0a05bfb, 0x5a5ab4ee, 0x3b3b764d, 0x5252a4f6, 0xb3b37dce, 0xd6d6b761, 0xe3e3dd3e, 0x2929527b, 0x84841397, 0x2f2f5e71,
     0xd1d1b968, 0x5353a6f5, 0xededc12c, 0x00000000, 0xfcfce31f, 0x20204060, 0x5b5bb6ed, 0xb1b179c8, 0xcbcb8d46, 0x6a6ad4be, 0x3939724b, 0xbebe67d9, 0x4c4c98d4, 0x4a4a94de, 0xcfcf854a, 0x5858b0e8,
     0xfdfde11c, 0xb7b775c2, 0x26264c6a, 0x93933dae, 0x3f3f7e41, 0x36366c5a, 0xcccc834f, 0xf7f7f502, 0xa5a551f4, 0x3434685c, 0xf1f1f908, 0xe5e5d134, 0xd8d8ab73, 0x7171e293, 0x15152a3f, 0x31316253,
     0xc7c79552, 0x0404080c, 0xc3c39d5e, 0x23234665, 0x969637a1, 0x18183028, 0x9a9a2fb5, 0x05050a0f, 0x12122436, 0x07070e09, 0xe2e2df3d, 0x80801b9b, 0x27274e69, 0xebebcd26, 0x7575ea9f, 0xb2b27fcd,
     0x7c7cf884, 0x6363c6a5, 0x7b7bf68d, 0x7777ee99, 0x6b6bd6bd, 0xf2f2ff0d, 0xc5c59154, 0x6f6fdeb1, 0x01010203, 0x30306050, 0x2b2b567d, 0x6767cea9, 0xd7d7b562, 0xfefee719, 0x7676ec9a, 0xabab4de6,
     0x82821f9d, 0xcaca8f45, 0x7d7dfa87, 0xc9c98940, 0x5959b2eb, 0xfafaef15, 0xf0f0fb0b, 0x47478ec9, 0xd4d4b367, 0xadad41ec, 0xafaf45ea, 0xa2a25ffd, 0xa4a453f7, 0x9c9c23bf, 0xc0c09b5b, 0x7272e496,
     0xf8f8eb13, 0xe1e1d938, 0x11112233, 0x98982bb3, 0xd9d9a970, 0x6969d2bb, 0x949433a7, 0x8e8e0789, 0x1e1e3c22, 0x9b9b2db6, 0xe9e9c920, 0x87871592, 0x5555aaff, 0xcece8749, 0xdfdfa57a, 0x28285078,
     0xa1a159f8, 0x8c8c038f, 0x0d0d1a17, 0x89890980, 0xe6e6d731, 0xbfbf65da, 0x6868d0b8, 0x424284c6, 0x999929b0, 0x414182c3, 0x0f0f1e11, 0x2d2d5a77, 0x5454a8fc, 0xb0b07bcb, 0x16162c3a, 0xbbbb6dd6,
     0x7878f088, 0xbaba6fd5, 0x2e2e5c72, 0x25254a6f, 0xa6a657f1, 0x1c1c3824, 0xc6c69751, 0xb4b473c7, 0xdddda17c, 0xe8e8cb23, 0x1f1f3e21, 0x7474e89c, 0xbdbd61dc, 0x4b4b96dd, 0x8a8a0f85, 0x8b8b0d86,
     0x3e3e7c42, 0x7070e090, 0x6666ccaa, 0xb5b571c4, 0x03030605, 0x484890d8, 0x0e0e1c12, 0xf6f6f701, 0x35356a5f, 0x6161c2a3, 0xb9b969d0, 0x5757aef9, 0xc1c19958, 0x86861791, 0x9e9e27b9, 0x1d1d3a27,
     0x32326456, 0xe0e0db3b, 0x0a0a141e, 0x3a3a744e, 0x06060c0a, 0x494992db, 0x5c5cb8e4, 0x2424486c, 0xd3d3bd6e, 0xc2c29f5d, 0x6262c4a6, 0xacac43ef, 0x959531a4, 0x919139a8, 0x7979f28b, 0xe4e4d337,
     0xc8c88b43, 0xe7e7d532, 0x6d6ddab7, 0x37376e59, 0xd5d5b164, 0x8d8d018c, 0xa9a949e0, 0x4e4e9cd2, 0x5656acfa, 0x6c6cd8b4, 0xeaeacf25, 0xf4f4f307, 0x7a7af48e, 0x6565caaf, 0x08081018, 0xaeae47e9,
     0x0c0c1814, 0xcdcd814c, 0xececc32f, 0x13132635, 0x979735a2, 0x5f5fbee1, 0x17172e39, 0x444488cc, 0xa7a755f2, 0xc4c49357, 0x3d3d7a47, 0x7e7efc82, 0x5d5dbae7, 0x6464c8ac, 0x7373e695, 0x1919322b,
     0x81811998, 0x6060c0a0, 0xdcdca37f, 0x4f4f9ed1, 0x2a2a547e, 0x22224466, 0x88880b83, 0x90903bab, 0xeeeec729, 0x46468cca, 0x1414283c, 0xb8b86bd3, 0x5e5ebce2, 0xdedea779, 0xdbdbad76, 0x0b0b161d
 ],
 [
     0x070e0907, 0x12243612, 0x801b9b80, 0xe2df3de2, 0xebcd26eb, 0x274e6927, 0xb27fcdb2, 0x75ea9f75, 0x04080c04, 0xc79552c7, 0x23466523, 0xc39d5ec3, 0x18302818, 0x9637a196, 0x050a0f05, 0x9a2fb59a,
     0x34685c34, 0xa551f4a5, 0xe5d134e5, 0xf1f908f1, 0x71e29371, 0xd8ab73d8, 0x31625331, 0x152a3f15, 0xb775c2b7, 0xfde11cfd, 0x933dae93, 0x264c6a26, 0x366c5a36, 0x3f7e413f, 0xf7f502f7, 0xcc834fcc,
     0xad41ecad, 0xd4b367d4, 0xa25ffda2, 0xaf45eaaf, 0x9c23bf9c, 0xa453f7a4, 0x72e49672, 0xc09b5bc0, 0xca8f45ca, 0x821f9d82, 0xc98940c9, 0x7dfa877d, 0xfaef15fa, 0x59b2eb59, 0x478ec947, 0xf0fb0bf0,
     0x30605030, 0x01020301, 0x67cea967, 0x2b567d2b, 0xfee719fe, 0xd7b562d7, 0xab4de6ab, 0x76ec9a76, 0x63c6a563, 0x7cf8847c, 0x77ee9977, 0x7bf68d7b, 0xf2ff0df2, 0x6bd6bd6b, 0x6fdeb16f, 0xc59154c5,
     0xbc63dfbc, 0xb677c1b6, 0xdaaf75da, 0x21426321, 0x10203010, 0xffe51aff, 0xf3fd0ef3, 0xd2bf6dd2, 0x51a2f351, 0xa35dfea3, 0x4080c040, 0x8f058a8f, 0x923fad92, 0x9d21bc9d, 0x38704838, 0xf5f104f5,
     0x458acf45, 0xf9e910f9, 0x02040602, 0x7ffe817f, 0x50a0f050, 0x3c78443c, 0x9f25ba9f, 0xa84be3a8, 0xd0bb6bd0, 0xefc52aef, 0xaa4fe5aa, 0xfbed16fb, 0x4386c543, 0x4d9ad74d, 0x33665533, 0x85119485,
     0x6ad4be6a, 0xcb8d46cb, 0xbe67d9be, 0x39724b39, 0x4a94de4a, 0x4c98d44c, 0x58b0e858, 0xcf854acf, 0x53a6f553, 0xd1b968d1, 0x00000000, 0xedc12ced, 0x20406020, 0xfce31ffc, 0xb179c8b1, 0x5bb6ed5b,
     0x52a4f652, 0x3b764d3b, 0xd6b761d6, 0xb37dceb3, 0x29527b29, 0xe3dd3ee3, 0x2f5e712f, 0x84139784, 0x09121b09, 0x831d9e83, 0x2c58742c, 0x1a342e1a, 0x1b362d1b, 0x6edcb26e, 0x5ab4ee5a, 0xa05bfba0,
     0x6cd8b46c, 0x56acfa56, 0xf4f307f4, 0xeacf25ea, 0x65caaf65, 0x7af48e7a, 0xae47e9ae, 0x08101808, 0xe7d532e7, 0xc88b43c8, 0x376e5937, 0x6ddab76d, 0x8d018c8d, 0xd5b164d5, 0x4e9cd24e, 0xa949e0a9,
     0xc29f5dc2, 0xd3bd6ed3, 0xac43efac, 0x62c4a662, 0x9139a891, 0x9531a495, 0xe4d337e4, 0x79f28b79, 0xe0db3be0, 0x32645632, 0x3a744e3a, 0x0a141e0a, 0x4992db49, 0x060c0a06, 0x24486c24, 0x5cb8e45c,
     0x468cca46, 0xeec729ee, 0xb86bd3b8, 0x14283c14, 0xdea779de, 0x5ebce25e, 0x0b161d0b, 0xdbad76db, 0x60c0a060, 0x81199881, 0x4f9ed14f, 0xdca37fdc, 0x22446622, 0x2a547e2a, 0x903bab90, 0x880b8388,
     0xc49357c4, 0xa755f2a7, 0x7efc827e, 0x3d7a473d, 0x64c8ac64, 0x5dbae75d, 0x19322b19, 0x73e69573, 0xcd814ccd, 0x0c18140c, 0x13263513, 0xecc32fec, 0x5fbee15f, 0x9735a297, 0x4488cc44, 0x172e3917,
     0x4182c341, 0x9929b099, 0x2d5a772d, 0x0f1e110f, 0xb07bcbb0, 0x54a8fc54, 0xbb6dd6bb, 0x162c3a16, 0x8c038f8c, 0xa159f8a1, 0x89098089, 0x0d1a170d, 0xbf65dabf, 0xe6d731e6, 0x4284c642, 0x68d0b868,
     0x9b2db69b, 0x1e3c221e, 0x87159287, 0xe9c920e9, 0xce8749ce, 0x55aaff55, 0x28507828, 0xdfa57adf, 0xe1d938e1, 0xf8eb13f8, 0x982bb398, 0x11223311, 0x69d2bb69, 0xd9a970d9, 0x8e07898e, 0x9433a794,
     0x61c2a361, 0x356a5f35, 0x57aef957, 0xb969d0b9, 0x86179186, 0xc19958c1, 0x1d3a271d, 0x9e27b99e, 0x70e09070, 0x3e7c423e, 0xb571c4b5, 0x66ccaa66, 0x4890d848, 0x03060503, 0xf6f701f6, 0x0e1c120e,
     0xe8cb23e8, 0xdda17cdd, 0x74e89c74, 0x1f3e211f, 0x4b96dd4b, 0xbd61dcbd, 0x8b0d868b, 0x8a0f858a, 0xba6fd5ba, 0x78f08878, 0x254a6f25, 0x2e5c722e, 0x1c38241c, 0xa657f1a6, 0xb473c7b4, 0xc69751c6
 ],
 [
     0xdcb26e6e, 0x362d1b1b, 0x5bfba0a0, 0xb4ee5a5a, 0x1d9e8383, 0x121b0909, 0x342e1a1a, 0x58742c2c, 0xdd3ee3e3, 0x527b2929, 0x13978484, 0x5e712f2f, 0x764d3b3b, 0xa4f65252, 0x7dceb3b3, 0xb761d6d6,
     0xe31ffcfc, 0x40602020, 0xb6ed5b5b, 0x79c8b1b1, 0xb968d1d1, 0xa6f55353, 0xc12ceded, 0x00000000, 0x98d44c4c, 0x94de4a4a, 0x854acfcf, 0xb0e85858, 0x8d46cbcb, 0xd4be6a6a, 0x724b3939, 0x67d9bebe,
     0x9ad74d4d, 0x86c54343, 0x11948585, 0x66553333, 0xc52aefef, 0xbb6bd0d0, 0xed16fbfb, 0x4fe5aaaa, 0x78443c3c, 0xa0f05050, 0x4be3a8a8, 0x25ba9f9f, 0xe910f9f9, 0x8acf4545, 0xfe817f7f, 0x04060202,
     0x21bc9d9d, 0x3fad9292, 0xf104f5f5, 0x70483838, 0x5dfea3a3, 0xa2f35151, 0x058a8f8f, 0x80c04040, 0xe51affff, 0x20301010, 0xbf6dd2d2, 0xfd0ef3f3, 0x77c1b6b6, 0x63dfbcbc, 0x42632121, 0xaf75dada,
     0xd6bd6b6b, 0xff0df2f2, 0x9154c5c5, 0xdeb16f6f, 0xf8847c7c, 0xc6a56363, 0xf68d7b7b, 0xee997777, 0xb562d7d7, 0xe719fefe, 0xec9a7676, 0x4de6abab, 0x02030101, 0x60503030, 0x567d2b2b, 0xcea96767,
     0xb2eb5959, 0xef15fafa, 0xfb0bf0f0, 0x8ec94747, 0x1f9d8282, 0x8f45caca, 0xfa877d7d, 0x8940c9c9, 0x53f7a4a4, 0x23bf9c9c, 0x9b5bc0c0, 0xe4967272, 0xb367d4d4, 0x41ecadad, 0x45eaafaf, 0x5ffda2a2,
     0x7e413f3f, 0x6c5a3636, 0x834fcccc, 0xf502f7f7, 0xe11cfdfd, 0x75c2b7b7, 0x4c6a2626, 0x3dae9393, 0xab73d8d8, 0xe2937171, 0x2a3f1515, 0x62533131, 0x51f4a5a5, 0x685c3434, 0xf908f1f1, 0xd134e5e5,
     0x37a19696, 0x30281818, 0x2fb59a9a, 0x0a0f0505, 0x9552c7c7, 0x080c0404, 0x9d5ec3c3, 0x46652323, 0x4e692727, 0xcd26ebeb, 0xea9f7575, 0x7fcdb2b2, 0x24361212, 0x0e090707, 0xdf3de2e2, 0x1b9b8080,
     0x57f1a6a6, 0x38241c1c, 0x9751c6c6, 0x73c7b4b4, 0xf0887878, 0x6fd5baba, 0x5c722e2e, 0x4a6f2525, 0x61dcbdbd, 0x96dd4b4b, 0x0f858a8a, 0x0d868b8b, 0xa17cdddd, 0xcb23e8e8, 0x3e211f1f, 0xe89c7474,
     0x06050303, 0x90d84848, 0x1c120e0e, 0xf701f6f6, 0x7c423e3e, 0xe0907070, 0xccaa6666, 0x71c4b5b5, 0x9958c1c1, 0x17918686, 0x27b99e9e, 0x3a271d1d, 0x6a5f3535, 0xc2a36161, 0x69d0b9b9, 0xaef95757,
     0xa970d9d9, 0xd2bb6969, 0x33a79494, 0x07898e8e, 0xeb13f8f8, 0xd938e1e1, 0x22331111, 0x2bb39898, 0xaaff5555, 0x8749cece, 0xa57adfdf, 0x50782828, 0x3c221e1e, 0x2db69b9b, 0xc920e9e9, 0x15928787,
     0xd731e6e6, 0x65dabfbf, 0xd0b86868, 0x84c64242, 0x59f8a1a1, 0x038f8c8c, 0x1a170d0d, 0x09808989, 0xa8fc5454, 0x7bcbb0b0, 0x2c3a1616, 0x6dd6bbbb, 0x29b09999, 0x82c34141, 0x1e110f0f, 0x5a772d2d,
     0x35a29797, 0xbee15f5f, 0x2e391717, 0x88cc4444, 0x18140c0c, 0x814ccdcd, 0xc32fecec, 0x26351313, 0xbae75d5d, 0xc8ac6464, 0xe6957373, 0x322b1919, 0x55f2a7a7, 0x9357c4c4, 0x7a473d3d, 0xfc827e7e,
     0x547e2a2a, 0x44662222, 0x0b838888, 0x3bab9090, 0x19988181, 0xc0a06060, 0xa37fdcdc, 0x9ed14f4f, 0xbce25e5e, 0xa779dede, 0xad76dbdb, 0x161d0b0b, 0xc729eeee, 0x8cca4646, 0x283c1414, 0x6bd3b8b8,
     0x0c0a0606, 0x92db4949, 0xb8e45c5c, 0x486c2424, 0x64563232, 0xdb3be0e0, 0x141e0a0a, 0x744e3a3a, 0x31a49595, 0x39a89191, 0xf28b7979, 0xd337e4e4, 0xbd6ed3d3, 0x9f5dc2c2, 0xc4a66262, 0x43efacac,
     0xb164d5d5, 0x018c8d8d, 0x49e0a9a9, 0x9cd24e4e, 0x8b43c8c8, 0xd532e7e7, 0xdab76d6d, 0x6e593737, 0xf48e7a7a, 0xcaaf6565, 0x10180808, 0x47e9aeae, 0xacfa5656, 0xd8b46c6c, 0xcf25eaea, 0xf307f4f4
 ],
 [
     0xeaafaf45, 0xfda2a25f, 0x67d4d4b3, 0xecadad41, 0x5bc0c09b, 0x967272e4, 0xf7a4a453, 0xbf9c9c23, 0x877d7dfa, 0x40c9c989, 0x9d82821f, 0x45caca8f, 0x0bf0f0fb, 0xc947478e, 0xeb5959b2, 0x15fafaef,
     0x7d2b2b56, 0xa96767ce, 0x03010102, 0x50303060, 0x9a7676ec, 0xe6abab4d, 0x62d7d7b5, 0x19fefee7, 0x8d7b7bf6, 0x997777ee, 0x847c7cf8, 0xa56363c6, 0x54c5c591, 0xb16f6fde, 0xbd6b6bd6, 0x0df2f2ff,
     0x3de2e2df, 0x9b80801b, 0x36121224, 0x0907070e, 0x9f7575ea, 0xcdb2b27f, 0x6927274e, 0x26ebebcd, 0x5ec3c39d, 0x65232346, 0x52c7c795, 0x0c040408, 0xb59a9a2f, 0x0f05050a, 0xa1969637, 0x28181830,
     0x08f1f1f9, 0x34e5e5d1, 0xf4a5a551, 0x5c343468, 0x3f15152a, 0x53313162, 0x73d8d8ab, 0x937171e2, 0x6a26264c, 0xae93933d, 0x1cfdfde1, 0xc2b7b775, 0x4fcccc83, 0x02f7f7f5, 0x413f3f7e, 0x5a36366c,
     0x4b393972, 0xd9bebe67, 0x46cbcb8d, 0xbe6a6ad4, 0x4acfcf85, 0xe85858b0, 0xd44c4c98, 0xde4a4a94, 0x2cededc1, 0x00000000, 0x68d1d1b9, 0xf55353a6, 0xed5b5bb6, 0xc8b1b179, 0x1ffcfce3, 0x60202040,
     0xceb3b37d, 0x61d6d6b7, 0x4d3b3b76, 0xf65252a4, 0x97848413, 0x712f2f5e, 0x3ee3e3dd, 0x7b292952, 0x2e1a1a34, 0x742c2c58, 0x9e83831d, 0x1b090912, 0xfba0a05b, 0xee5a5ab4, 0xb26e6edc, 0x2d1b1b36,
     0x63212142, 0x75dadaaf, 0xc1b6b677, 0xdfbcbc63, 0x6dd2d2bf, 0x0ef3f3fd, 0x1affffe5, 0x30101020, 0x8a8f8f05, 0xc0404080, 0xfea3a35d, 0xf35151a2, 0x04f5f5f1, 0x48383870, 0xbc9d9d21, 0xad92923f,
     0x817f7ffe, 0x06020204, 0x10f9f9e9, 0xcf45458a, 0xe3a8a84b, 0xba9f9f25, 0x443c3c78, 0xf05050a0, 0x16fbfbed, 0xe5aaaa4f, 0x2aefefc5, 0x6bd0d0bb, 0x94858511, 0x55333366, 0xd74d4d9a, 0xc5434386,
     0x3c141428, 0xd3b8b86b, 0x29eeeec7, 0xca46468c, 0x76dbdbad, 0x1d0b0b16, 0xe25e5ebc, 0x79dedea7, 0x7fdcdca3, 0xd14f4f9e, 0x98818119, 0xa06060c0, 0x8388880b, 0xab90903b, 0x7e2a2a54, 0x66222244,
     0x473d3d7a, 0x827e7efc, 0xf2a7a755, 0x57c4c493, 0x957373e6, 0x2b191932, 0xe75d5dba, 0xac6464c8, 0x2fececc3, 0x35131326, 0x140c0c18, 0x4ccdcd81, 0x3917172e, 0xcc444488, 0xa2979735, 0xe15f5fbe,
     0x25eaeacf, 0x07f4f4f3, 0xfa5656ac, 0xb46c6cd8, 0x18080810, 0xe9aeae47, 0x8e7a7af4, 0xaf6565ca, 0xb76d6dda, 0x5937376e, 0x43c8c88b, 0x32e7e7d5, 0xe0a9a949, 0xd24e4e9c, 0x64d5d5b1, 0x8c8d8d01,
     0xa66262c4, 0xefacac43, 0x6ed3d3bd, 0x5dc2c29f, 0x8b7979f2, 0x37e4e4d3, 0xa4959531, 0xa8919139, 0x1e0a0a14, 0x4e3a3a74, 0x56323264, 0x3be0e0db, 0xe45c5cb8, 0x6c242448, 0x0a06060c, 0xdb494992,
     0xd0b9b969, 0xf95757ae, 0x5f35356a, 0xa36161c2, 0xb99e9e27, 0x271d1d3a, 0x58c1c199, 0x91868617, 0xaa6666cc, 0xc4b5b571, 0x423e3e7c, 0x907070e0, 0x120e0e1c, 0x01f6f6f7, 0x05030306, 0xd8484890,
     0x211f1f3e, 0x9c7474e8, 0x7cdddda1, 0x23e8e8cb, 0x858a8a0f, 0x868b8b0d, 0xdcbdbd61, 0xdd4b4b96, 0x722e2e5c, 0x6f25254a, 0x887878f0, 0xd5baba6f, 0x51c6c697, 0xc7b4b473, 0xf1a6a657, 0x241c1c38,
     0x110f0f1e, 0x772d2d5a, 0xb0999929, 0xc3414182, 0x3a16162c, 0xd6bbbb6d, 0xfc5454a8, 0xcbb0b07b, 0x170d0d1a, 0x80898909, 0xf8a1a159, 0x8f8c8c03, 0xb86868d0, 0xc6424284, 0x31e6e6d7, 0xdabfbf65,
     0x20e9e9c9, 0x92878715, 0x221e1e3c, 0xb69b9b2d, 0x7adfdfa5, 0x78282850, 0xff5555aa, 0x49cece87, 0x33111122, 0xb398982b, 0x13f8f8eb, 0x38e1e1d9, 0xa7949433, 0x898e8e07, 0x70d9d9a9, 0xbb6969d2
 ],
 [
     0x404080c0, 0x8f8f058a, 0x5151a2f3, 0xa3a35dfe, 0x38387048, 0xf5f5f104, 0x92923fad, 0x9d9d21bc, 0xdadaaf75, 0x21214263, 0xbcbc63df, 0xb6b677c1, 0xf3f3fd0e, 0xd2d2bf6d, 0x10102030, 0xffffe51a,
     0xaaaa4fe5, 0xfbfbed16, 0xd0d0bb6b, 0xefefc52a, 0x33336655, 0x85851194, 0x434386c5, 0x4d4d9ad7, 0x02020406, 0x7f7ffe81, 0x45458acf, 0xf9f9e910, 0x9f9f25ba, 0xa8a84be3, 0x5050a0f0, 0x3c3c7844,
     0x00000000, 0xededc12c, 0x5353a6f5, 0xd1d1b968, 0xb1b179c8, 0x5b5bb6ed, 0x20204060, 0xfcfce31f, 0xbebe67d9, 0x3939724b, 0x6a6ad4be, 0xcbcb8d46, 0x5858b0e8, 0xcfcf854a, 0x4a4a94de, 0x4c4c98d4,
     0x2c2c5874, 0x1a1a342e, 0x0909121b, 0x83831d9e, 0x5a5ab4ee, 0xa0a05bfb, 0x1b1b362d, 0x6e6edcb2, 0xd6d6b761, 0xb3b37dce, 0x5252a4f6, 0x3b3b764d, 0x2f2f5e71, 0x84841397, 0x2929527b, 0xe3e3dd3e,
     0x23234665, 0xc3c39d5e, 0x0404080c, 0xc7c79552, 0x05050a0f, 0x9a9a2fb5, 0x18183028, 0x969637a1, 0x80801b9b, 0xe2e2df3d, 0x07070e09, 0x12122436, 0xb2b27fcd, 0x7575ea9f, 0xebebcd26, 0x27274e69,
     0x93933dae, 0x26264c6a, 0xb7b775c2, 0xfdfde11c, 0xf7f7f502, 0xcccc834f, 0x36366c5a, 0x3f3f7e41, 0xe5e5d134, 0xf1f1f908, 0x3434685c, 0xa5a551f4, 0x31316253, 0x15152a3f, 0x7171e293, 0xd8d8ab73,
     0xc9c98940, 0x7d7dfa87, 0xcaca8f45, 0x82821f9d, 0x47478ec9, 0xf0f0fb0b, 0xfafaef15, 0x5959b2eb, 0xa2a25ffd, 0xafaf45ea, 0xadad41ec, 0xd4d4b367, 0x7272e496, 0xc0c09b5b, 0x9c9c23bf, 0xa4a453f7,
     0x7777ee99, 0x7b7bf68d, 0x6363c6a5, 0x7c7cf884, 0x6f6fdeb1, 0xc5c59154, 0xf2f2ff0d, 0x6b6bd6bd, 0x6767cea9, 0x2b2b567d, 0x30306050, 0x01010203, 0xabab4de6, 0x7676ec9a, 0xfefee719, 0xd7d7b562,
     0x89890980, 0x0d0d1a17, 0x8c8c038f, 0xa1a159f8, 0x424284c6, 0x6868d0b8, 0xbfbf65da, 0xe6e6d731, 0x2d2d5a77, 0x0f0f1e11, 0x414182c3, 0x999929b0, 0xbbbb6dd6, 0x16162c3a, 0xb0b07bcb, 0x5454a8fc,
     0x98982bb3, 0x11112233, 0xe1e1d938, 0xf8f8eb13, 0x8e8e0789, 0x949433a7, 0x6969d2bb, 0xd9d9a970, 0x87871592, 0xe9e9c920, 0x9b9b2db6, 0x1e1e3c22, 0x28285078, 0xdfdfa57a, 0xcece8749, 0x5555aaff,
     0xb5b571c4, 0x6666ccaa, 0x7070e090, 0x3e3e7c42, 0xf6f6f701, 0x0e0e1c12, 0x484890d8, 0x03030605, 0x5757aef9, 0xb9b969d0, 0x6161c2a3, 0x35356a5f, 0x1d1d3a27, 0x9e9e27b9, 0x86861791, 0xc1c19958,
     0x25254a6f, 0x2e2e5c72, 0xbaba6fd5, 0x7878f088, 0xb4b473c7, 0xc6c69751, 0x1c1c3824, 0xa6a657f1, 0x7474e89c, 0x1f1f3e21, 0xe8e8cb23, 0xdddda17c, 0x8b8b0d86, 0x8a8a0f85, 0x4b4b96dd, 0xbdbd61dc,
     0x37376e59, 0x6d6ddab7, 0xe7e7d532, 0xc8c88b43, 0x4e4e9cd2, 0xa9a949e0, 0x8d8d018c, 0xd5d5b164, 0xf4f4f307, 0xeaeacf25, 0x6c6cd8b4, 0x5656acfa, 0xaeae47e9, 0x08081018, 0x6565caaf, 0x7a7af48e,
     0x3a3a744e, 0x0a0a141e, 0xe0e0db3b, 0x32326456, 0x2424486c, 0x5c5cb8e4, 0x494992db, 0x06060c0a, 0xacac43ef, 0x6262c4a6, 0xc2c29f5d, 0xd3d3bd6e, 0xe4e4d337, 0x7979f28b, 0x919139a8, 0x959531a4,
     0x4f4f9ed1, 0xdcdca37f, 0x6060c0a0, 0x81811998, 0x90903bab, 0x88880b83, 0x22224466, 0x2a2a547e, 0xb8b86bd3, 0x1414283c, 0x46468cca, 0xeeeec729, 0x0b0b161d, 0xdbdbad76, 0xdedea779, 0x5e5ebce2,
     0x13132635, 0xececc32f, 0xcdcd814c, 0x0c0c1814, 0x444488cc, 0x17172e39, 0x5f5fbee1, 0x979735a2, 0x7e7efc82, 0x3d3d7a47, 0xc4c49357, 0xa7a755f2, 0x1919322b, 0x7373e695, 0x6464c8ac, 0x5d5dbae7
 ],
 [
     0x3b764d3b, 0x52a4f652, 0xb37dceb3, 0xd6b761d6, 0xe3dd3ee3, 0x29527b29, 0x84139784, 0x2f5e712f, 0x831d9e83, 0x09121b09, 0x1a342e1a, 0x2c58742c, 0x6edcb26e, 0x1b362d1b, 0xa05bfba0, 0x5ab4ee5a,
     0xcb8d46cb, 0x6ad4be6a, 0x39724b39, 0xbe67d9be, 0x4c98d44c, 0x4a94de4a, 0xcf854acf, 0x58b0e858, 0xd1b968d1, 0x53a6f553, 0xedc12ced, 0x00000000, 0xfce31ffc, 0x20406020, 0x5bb6ed5b, 0xb179c8b1,
     0xf9e910f9, 0x458acf45, 0x7ffe817f, 0x02040602, 0x3c78443c, 0x50a0f050, 0xa84be3a8, 0x9f25ba9f, 0xefc52aef, 0xd0bb6bd0, 0xfbed16fb, 0xaa4fe5aa, 0x4d9ad74d, 0x4386c543, 0x85119485, 0x33665533,
     0xb677c1b6, 0xbc63dfbc, 0x21426321, 0xdaaf75da, 0xffe51aff, 0x10203010, 0xd2bf6dd2, 0xf3fd0ef3, 0xa35dfea3, 0x51a2f351, 0x8f058a8f, 0x4080c040, 0x9d21bc9d, 0x923fad92, 0xf5f104f5, 0x38704838,
     0x01020301, 0x30605030, 0x2b567d2b, 0x67cea967, 0xd7b562d7, 0xfee719fe, 0x76ec9a76, 0xab4de6ab, 0x7cf8847c, 0x63c6a563, 0x7bf68d7b, 0x77ee9977, 0x6bd6bd6b, 0xf2ff0df2, 0xc59154c5, 0x6fdeb16f,
     0xd4b367d4, 0xad41ecad, 0xaf45eaaf, 0xa25ffda2, 0xa453f7a4, 0x9c23bf9c, 0xc09b5bc0, 0x72e49672, 0x821f9d82, 0xca8f45ca, 0x7dfa877d, 0xc98940c9, 0x59b2eb59, 0xfaef15fa, 0xf0fb0bf0, 0x478ec947,
     0xa551f4a5, 0x34685c34, 0xf1f908f1, 0xe5d134e5, 0xd8ab73d8, 0x71e29371, 0x152a3f15, 0x31625331, 0xfde11cfd, 0xb775c2b7, 0x264c6a26, 0x933dae93, 0x3f7e413f, 0x366c5a36, 0xcc834fcc, 0xf7f502f7,
     0x12243612, 0x070e0907, 0xe2df3de2, 0x801b9b80, 0x274e6927, 0xebcd26eb, 0x75ea9f75, 0xb27fcdb2, 0xc79552c7, 0x04080c04, 0xc39d5ec3, 0x23466523, 0x9637a196, 0x18302818, 0x9a2fb59a, 0x050a0f05,
     0xdda17cdd, 0xe8cb23e8, 0x1f3e211f, 0x74e89c74, 0xbd61dcbd, 0x4b96dd4b, 0x8a0f858a, 0x8b0d868b, 0x78f08878, 0xba6fd5ba, 0x2e5c722e, 0x254a6f25, 0xa657f1a6, 0x1c38241c, 0xc69751c6, 0xb473c7b4,
     0x356a5f35, 0x61c2a361, 0xb969d0b9, 0x57aef957, 0xc19958c1, 0x86179186, 0x9e27b99e, 0x1d3a271d, 0x3e7c423e, 0x70e09070, 0x66ccaa66, 0xb571c4b5, 0x03060503, 0x4890d848, 0x0e1c120e, 0xf6f701f6,
     0x1e3c221e, 0x9b2db69b, 0xe9c920e9, 0x87159287, 0x55aaff55, 0xce8749ce, 0xdfa57adf, 0x28507828, 0xf8eb13f8, 0xe1d938e1, 0x11223311, 0x982bb398, 0xd9a970d9, 0x69d2bb69, 0x9433a794, 0x8e07898e,
     0x9929b099, 0x4182c341, 0x0f1e110f, 0x2d5a772d, 0x54a8fc54, 0xb07bcbb0, 0x162c3a16, 0xbb6dd6bb, 0xa159f8a1, 0x8c038f8c, 0x0d1a170d, 0x89098089, 0xe6d731e6, 0xbf65dabf, 0x68d0b868, 0x4284c642,
     0xa755f2a7, 0xc49357c4, 0x3d7a473d, 0x7efc827e, 0x5dbae75d, 0x64c8ac64, 0x73e69573, 0x19322b19, 0x0c18140c, 0xcd814ccd, 0xecc32fec, 0x13263513, 0x9735a297, 0x5fbee15f, 0x172e3917, 0x4488cc44,
     0xeec729ee, 0x468cca46, 0x14283c14, 0xb86bd3b8, 0x5ebce25e, 0xdea779de, 0xdbad76db, 0x0b161d0b, 0x81199881, 0x60c0a060, 0xdca37fdc, 0x4f9ed14f, 0x2a547e2a, 0x22446622, 0x880b8388, 0x903bab90,
     0xd3bd6ed3, 0xc29f5dc2, 0x62c4a662, 0xac43efac, 0x9531a495, 0x9139a891, 0x79f28b79, 0xe4d337e4, 0x32645632, 0xe0db3be0, 0x0a141e0a, 0x3a744e3a, 0x060c0a06, 0x4992db49, 0x5cb8e45c, 0x24486c24,
     0x56acfa56, 0x6cd8b46c, 0xeacf25ea, 0xf4f307f4, 0x7af48e7a, 0x65caaf65, 0x08101808, 0xae47e9ae, 0xc88b43c8, 0xe7d532e7, 0x6ddab76d, 0x376e5937, 0xd5b164d5, 0x8d018c8d, 0xa949e0a9, 0x4e9cd24e
 ],
 [
     0x09808989, 0x1a170d0d, 0x038f8c8c, 0x59f8a1a1, 0x84c64242, 0xd0b86868, 0x65dabfbf, 0xd731e6e6, 0x5a772d2d, 0x1e110f0f, 0x82c34141, 0x29b09999, 0x6dd6bbbb, 0x2c3a1616, 0x7bcbb0b0, 0xa8fc5454,
     0x2bb39898, 0x22331111, 0xd938e1e1, 0xeb13f8f8, 0x07898e8e, 0x33a79494, 0xd2bb6969, 0xa970d9d9, 0x15928787, 0xc920e9e9, 0x2db69b9b, 0x3c221e1e, 0x50782828, 0xa57adfdf, 0x8749cece, 0xaaff5555,
     0x71c4b5b5, 0xccaa6666, 0xe0907070, 0x7c423e3e, 0xf701f6f6, 0x1c120e0e, 0x90d84848, 0x06050303, 0xaef95757, 0x69d0b9b9, 0xc2a36161, 0x6a5f3535, 0x3a271d1d, 0x27b99e9e, 0x17918686, 0x9958c1c1,
     0x4a6f2525, 0x5c722e2e, 0x6fd5baba, 0xf0887878, 0x73c7b4b4, 0x9751c6c6, 0x38241c1c, 0x57f1a6a6, 0xe89c7474, 0x3e211f1f, 0xcb23e8e8, 0xa17cdddd, 0x0d868b8b, 0x0f858a8a, 0x96dd4b4b, 0x61dcbdbd,
     0x6e593737, 0xdab76d6d, 0xd532e7e7, 0x8b43c8c8, 0x9cd24e4e, 0x49e0a9a9, 0x018c8d8d, 0xb164d5d5, 0xf307f4f4, 0xcf25eaea, 0xd8b46c6c, 0xacfa5656, 0x47e9aeae, 0x10180808, 0xcaaf6565, 0xf48e7a7a,
     0x744e3a3a, 0x141e0a0a, 0xdb3be0e0, 0x64563232, 0x486c2424, 0xb8e45c5c, 0x92db4949, 0x0c0a0606, 0x43efacac, 0xc4a66262, 0x9f5dc2c2, 0xbd6ed3d3, 0xd337e4e4, 0xf28b7979, 0x39a89191, 0x31a49595,
     0x9ed14f4f, 0xa37fdcdc, 0xc0a06060, 0x19988181, 0x3bab9090, 0x0b838888, 0x44662222, 0x547e2a2a, 0x6bd3b8b8, 0x283c1414, 0x8cca4646, 0xc729eeee, 0x161d0b0b, 0xad76dbdb, 0xa779dede, 0xbce25e5e,
     0x26351313, 0xc32fecec, 0x814ccdcd, 0x18140c0c, 0x88cc4444, 0x2e391717, 0xbee15f5f, 0x35a29797, 0xfc827e7e, 0x7a473d3d, 0x9357c4c4, 0x55f2a7a7, 0x322b1919, 0xe6957373, 0xc8ac6464, 0xbae75d5d,
     0x80c04040, 0x058a8f8f, 0xa2f35151, 0x5dfea3a3, 0x70483838, 0xf104f5f5, 0x3fad9292, 0x21bc9d9d, 0xaf75dada, 0x42632121, 0x63dfbcbc, 0x77c1b6b6, 0xfd0ef3f3, 0xbf6dd2d2, 0x20301010, 0xe51affff,
     0x4fe5aaaa, 0xed16fbfb, 0xbb6bd0d0, 0xc52aefef, 0x66553333, 0x11948585, 0x86c54343, 0x9ad74d4d, 0x04060202, 0xfe817f7f, 0x8acf4545, 0xe910f9f9, 0x25ba9f9f, 0x4be3a8a8, 0xa0f05050, 0x78443c3c,
     0x00000000, 0xc12ceded, 0xa6f55353, 0xb968d1d1, 0x79c8b1b1, 0xb6ed5b5b, 0x40602020, 0xe31ffcfc, 0x67d9bebe, 0x724b3939, 0xd4be6a6a, 0x8d46cbcb, 0xb0e85858, 0x854acfcf, 0x94de4a4a, 0x98d44c4c,
     0x58742c2c, 0x342e1a1a, 0x121b0909, 0x1d9e8383, 0xb4ee5a5a, 0x5bfba0a0, 0x362d1b1b, 0xdcb26e6e, 0xb761d6d6, 0x7dceb3b3, 0xa4f65252, 0x764d3b3b, 0x5e712f2f, 0x13978484, 0x527b2929, 0xdd3ee3e3,
     0x46652323, 0x9d5ec3c3, 0x080c0404, 0x9552c7c7, 0x0a0f0505, 0x2fb59a9a, 0x30281818, 0x37a19696, 0x1b9b8080, 0xdf3de2e2, 0x0e090707, 0x24361212, 0x7fcdb2b2, 0xea9f7575, 0xcd26ebeb, 0x4e692727,
     0x3dae9393, 0x4c6a2626, 0x75c2b7b7, 0xe11cfdfd, 0xf502f7f7, 0x834fcccc, 0x6c5a3636, 0x7e413f3f, 0xd134e5e5, 0xf908f1f1, 0x685c3434, 0x51f4a5a5, 0x62533131, 0x2a3f1515, 0xe2937171, 0xab73d8d8,
     0x8940c9c9, 0xfa877d7d, 0x8f45caca, 0x1f9d8282, 0x8ec94747, 0xfb0bf0f0, 0xef15fafa, 0xb2eb5959, 0x5ffda2a2, 0x45eaafaf, 0x41ecadad, 0xb367d4d4, 0xe4967272, 0x9b5bc0c0, 0x23bf9c9c, 0x53f7a4a4,
     0xee997777, 0xf68d7b7b, 0xc6a56363, 0xf8847c7c, 0xdeb16f6f, 0x9154c5c5, 0xff0df2f2, 0xd6bd6b6b, 0xcea96767, 0x567d2b2b, 0x60503030, 0x02030101, 0x4de6abab, 0xec9a7676, 0xe719fefe, 0xb562d7d7
 ],
 [
     0xc8b1b179, 0xed5b5bb6, 0x60202040, 0x1ffcfce3, 0x00000000, 0x2cededc1, 0xf55353a6, 0x68d1d1b9, 0xe85858b0, 0x4acfcf85, 0xde4a4a94, 0xd44c4c98, 0xd9bebe67, 0x4b393972, 0xbe6a6ad4, 0x46cbcb8d,
     0xee5a5ab4, 0xfba0a05b, 0x2d1b1b36, 0xb26e6edc, 0x742c2c58, 0x2e1a1a34, 0x1b090912, 0x9e83831d, 0x712f2f5e, 0x97848413, 0x7b292952, 0x3ee3e3dd, 0x61d6d6b7, 0xceb3b37d, 0xf65252a4, 0x4d3b3b76,
     0x48383870, 0x04f5f5f1, 0xad92923f, 0xbc9d9d21, 0xc0404080, 0x8a8f8f05, 0xf35151a2, 0xfea3a35d, 0x0ef3f3fd, 0x6dd2d2bf, 0x30101020, 0x1affffe5, 0x75dadaaf, 0x63212142, 0xdfbcbc63, 0xc1b6b677,
     0x55333366, 0x94858511, 0xc5434386, 0xd74d4d9a, 0xe5aaaa4f, 0x16fbfbed, 0x6bd0d0bb, 0x2aefefc5, 0xba9f9f25, 0xe3a8a84b, 0xf05050a0, 0x443c3c78, 0x06020204, 0x817f7ffe, 0xcf45458a, 0x10f9f9e9,
     0xc947478e, 0x0bf0f0fb, 0x15fafaef, 0xeb5959b2, 0x40c9c989, 0x877d7dfa, 0x45caca8f, 0x9d82821f, 0x967272e4, 0x5bc0c09b, 0xbf9c9c23, 0xf7a4a453, 0xfda2a25f, 0xeaafaf45, 0xecadad41, 0x67d4d4b3,
     0xb16f6fde, 0x54c5c591, 0x0df2f2ff, 0xbd6b6bd6, 0x997777ee, 0x8d7b7bf6, 0xa56363c6, 0x847c7cf8, 0xe6abab4d, 0x9a7676ec, 0x19fefee7, 0x62d7d7b5, 0xa96767ce, 0x7d2b2b56, 0x50303060, 0x03010102,
     0x0f05050a, 0xb59a9a2f, 0x28181830, 0xa1969637, 0x65232346, 0x5ec3c39d, 0x0c040408, 0x52c7c795, 0xcdb2b27f, 0x9f7575ea, 0x26ebebcd, 0x6927274e, 0x9b80801b, 0x3de2e2df, 0x0907070e, 0x36121224,
     0x02f7f7f5, 0x4fcccc83, 0x5a36366c, 0x413f3f7e, 0xae93933d, 0x6a26264c, 0xc2b7b775, 0x1cfdfde1, 0x53313162, 0x3f15152a, 0x937171e2, 0x73d8d8ab, 0x34e5e5d1, 0x08f1f1f9, 0x5c343468, 0xf4a5a551,
     0x01f6f6f7, 0x120e0e1c, 0xd8484890, 0x05030306, 0xc4b5b571, 0xaa6666cc, 0x907070e0, 0x423e3e7c, 0x271d1d3a, 0xb99e9e27, 0x91868617, 0x58c1c199, 0xf95757ae, 0xd0b9b969, 0xa36161c2, 0x5f35356a,
     0xc7b4b473, 0x51c6c697, 0x241c1c38, 0xf1a6a657, 0x6f25254a, 0x722e2e5c, 0xd5baba6f, 0x887878f0, 0x868b8b0d, 0x858a8a0f, 0xdd4b4b96, 0xdcbdbd61, 0x9c7474e8, 0x211f1f3e, 0x23e8e8cb, 0x7cdddda1,
     0xc6424284, 0xb86868d0, 0xdabfbf65, 0x31e6e6d7, 0x80898909, 0x170d0d1a, 0x8f8c8c03, 0xf8a1a159, 0xd6bbbb6d, 0x3a16162c, 0xcbb0b07b, 0xfc5454a8, 0x772d2d5a, 0x110f0f1e, 0xc3414182, 0xb0999929,
     0x898e8e07, 0xa7949433, 0xbb6969d2, 0x70d9d9a9, 0xb398982b, 0x33111122, 0x38e1e1d9, 0x13f8f8eb, 0x78282850, 0x7adfdfa5, 0x49cece87, 0xff5555aa, 0x92878715, 0x20e9e9c9, 0xb69b9b2d, 0x221e1e3c,
     0xab90903b, 0x8388880b, 0x66222244, 0x7e2a2a54, 0xd14f4f9e, 0x7fdcdca3, 0xa06060c0, 0x98818119, 0x1d0b0b16, 0x76dbdbad, 0x79dedea7, 0xe25e5ebc, 0xd3b8b86b, 0x3c141428, 0xca46468c, 0x29eeeec7,
     0xcc444488, 0x3917172e, 0xe15f5fbe, 0xa2979735, 0x35131326, 0x2fececc3, 0x4ccdcd81, 0x140c0c18, 0x2b191932, 0x957373e6, 0xac6464c8, 0xe75d5dba, 0x827e7efc, 0x473d3d7a, 0x57c4c493, 0xf2a7a755,
     0xd24e4e9c, 0xe0a9a949, 0x8c8d8d01, 0x64d5d5b1, 0x5937376e, 0xb76d6dda, 0x32e7e7d5, 0x43c8c88b, 0xe9aeae47, 0x18080810, 0xaf6565ca, 0x8e7a7af4, 0x07f4f4f3, 0x25eaeacf, 0xb46c6cd8, 0xfa5656ac,
     0x6c242448, 0xe45c5cb8, 0xdb494992, 0x0a06060c, 0x4e3a3a74, 0x1e0a0a14, 0x3be0e0db, 0x56323264, 0x37e4e4d3, 0x8b7979f2, 0xa8919139, 0xa4959531, 0xefacac43, 0xa66262c4, 0x5dc2c29f, 0x6ed3d3bd
 ],
 [
     0xadad41ec, 0xd4d4b367, 0xa2a25ffd, 0xafaf45ea, 0x9c9c23bf, 0xa4a453f7, 0x7272e496, 0xc0c09b5b, 0xcaca8f45, 0x82821f9d, 0xc9c98940, 0x7d7dfa87, 0xfafaef15, 0x5959b2eb, 0x47478ec9, 0xf0f0fb0b,
     0x30306050, 0x01010203, 0x6767cea9, 0x2b2b567d, 0xfefee719, 0xd7d7b562, 0xabab4de6, 0x7676ec9a, 0x6363c6a5, 0x7c7cf884, 0x7777ee99, 0x7b7bf68d, 0xf2f2ff0d, 0x6b6bd6bd, 0x6f6fdeb1, 0xc5c59154,
     0x07070e09, 0x12122436, 0x80801b9b, 0xe2e2df3d, 0xebebcd26, 0x27274e69, 0xb2b27fcd, 0x7575ea9f, 0x0404080c, 0xc7c79552, 0x23234665, 0xc3c39d5e, 0x18183028, 0x969637a1, 0x05050a0f, 0x9a9a2fb5,
     0x3434685c, 0xa5a551f4, 0xe5e5d134, 0xf1f1f908, 0x7171e293, 0xd8d8ab73, 0x31316253, 0x15152a3f, 0xb7b775c2, 0xfdfde11c, 0x93933dae, 0x26264c6a, 0x36366c5a, 0x3f3f7e41, 0xf7f7f502, 0xcccc834f,
     0x6a6ad4be, 0xcbcb8d46, 0xbebe67d9, 0x3939724b, 0x4a4a94de, 0x4c4c98d4, 0x5858b0e8, 0xcfcf854a, 0x5353a6f5, 0xd1d1b968, 0x00000000, 0xededc12c, 0x20204060, 0xfcfce31f, 0xb1b179c8, 0x5b5bb6ed,
     0x5252a4f6, 0x3b3b764d, 0xd6d6b761, 0xb3b37dce, 0x2929527b, 0xe3e3dd3e, 0x2f2f5e71, 0x84841397, 0x0909121b, 0x83831d9e, 0x2c2c5874, 0x1a1a342e, 0x1b1b362d, 0x6e6edcb2, 0x5a5ab4ee, 0xa0a05bfb,
     0xbcbc63df, 0xb6b677c1, 0xdadaaf75, 0x21214263, 0x10102030, 0xffffe51a, 0xf3f3fd0e, 0xd2d2bf6d, 0x5151a2f3, 0xa3a35dfe, 0x404080c0, 0x8f8f058a, 0x92923fad, 0x9d9d21bc, 0x38387048, 0xf5f5f104,
     0x45458acf, 0xf9f9e910, 0x02020406, 0x7f7ffe81, 0x5050a0f0, 0x3c3c7844, 0x9f9f25ba, 0xa8a84be3, 0xd0d0bb6b, 0xefefc52a, 0xaaaa4fe5, 0xfbfbed16, 0x434386c5, 0x4d4d9ad7, 0x33336655, 0x85851194,
     0x46468cca, 0xeeeec729, 0xb8b86bd3, 0x1414283c, 0xdedea779, 0x5e5ebce2, 0x0b0b161d, 0xdbdbad76, 0x6060c0a0, 0x81811998, 0x4f4f9ed1, 0xdcdca37f, 0x22224466, 0x2a2a547e, 0x90903bab, 0x88880b83,
     0xc4c49357, 0xa7a755f2, 0x7e7efc82, 0x3d3d7a47, 0x6464c8ac, 0x5d5dbae7, 0x1919322b, 0x7373e695, 0xcdcd814c, 0x0c0c1814, 0x13132635, 0xececc32f, 0x5f5fbee1, 0x979735a2, 0x444488cc, 0x17172e39,
     0x6c6cd8b4, 0x5656acfa, 0xf4f4f307, 0xeaeacf25, 0x6565caaf, 0x7a7af48e, 0xaeae47e9, 0x08081018, 0xe7e7d532, 0xc8c88b43, 0x37376e59, 0x6d6ddab7, 0x8d8d018c, 0xd5d5b164, 0x4e4e9cd2, 0xa9a949e0,
     0xc2c29f5d, 0xd3d3bd6e, 0xacac43ef, 0x6262c4a6, 0x919139a8, 0x959531a4, 0xe4e4d337, 0x7979f28b, 0xe0e0db3b, 0x32326456, 0x3a3a744e, 0x0a0a141e, 0x494992db, 0x06060c0a, 0x2424486c, 0x5c5cb8e4,
     0x6161c2a3, 0x35356a5f, 0x5757aef9, 0xb9b969d0, 0x86861791, 0xc1c19958, 0x1d1d3a27, 0x9e9e27b9, 0x7070e090, 0x3e3e7c42, 0xb5b571c4, 0x6666ccaa, 0x484890d8, 0x03030605, 0xf6f6f701, 0x0e0e1c12,
     0xe8e8cb23, 0xdddda17c, 0x7474e89c, 0x1f1f3e21, 0x4b4b96dd, 0xbdbd61dc, 0x8b8b0d86, 0x8a8a0f85, 0xbaba6fd5, 0x7878f088, 0x25254a6f, 0x2e2e5c72, 0x1c1c3824, 0xa6a657f1, 0xb4b473c7, 0xc6c69751,
     0x414182c3, 0x999929b0, 0x2d2d5a77, 0x0f0f1e11, 0xb0b07bcb, 0x5454a8fc, 0xbbbb6dd6, 0x16162c3a, 0x8c8c038f, 0xa1a159f8, 0x89890980, 0x0d0d1a17, 0xbfbf65da, 0xe6e6d731, 0x424284c6, 0x6868d0b8,
     0x9b9b2db6, 0x1e1e3c22, 0x87871592, 0xe9e9c920, 0xcece8749, 0x5555aaff, 0x28285078, 0xdfdfa57a, 0xe1e1d938, 0xf8f8eb13, 0x98982bb3, 0x11112233, 0x6969d2bb, 0xd9d9a970, 0x8e8e0789, 0x949433a7
 ],
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     0xdca37fdc, 0x4f9ed14f, 0x81199881, 0x60c0a060, 0x880b8388, 0x903bab90, 0x2a547e2a, 0x22446622, 0x14283c14, 0xb86bd3b8, 0xeec729ee, 0x468cca46, 0xdbad76db, 0x0b161d0b, 0x5ebce25e, 0xdea779de,
     0xecc32fec, 0x13263513, 0x0c18140c, 0xcd814ccd, 0x172e3917, 0x4488cc44, 0x9735a297, 0x5fbee15f, 0x3d7a473d, 0x7efc827e, 0xa755f2a7, 0xc49357c4, 0x73e69573, 0x19322b19, 0x5dbae75d, 0x64c8ac64,
     0x6ddab76d, 0x376e5937, 0xc88b43c8, 0xe7d532e7, 0xa949e0a9, 0x4e9cd24e, 0xd5b164d5, 0x8d018c8d, 0xeacf25ea, 0xf4f307f4, 0x56acfa56, 0x6cd8b46c, 0x08101808, 0xae47e9ae, 0x7af48e7a, 0x65caaf65,
     0x0a141e0a, 0x3a744e3a, 0x32645632, 0xe0db3be0, 0x5cb8e45c, 0x24486c24, 0x060c0a06, 0x4992db49, 0x62c4a662, 0xac43efac, 0xd3bd6ed3, 0xc29f5dc2, 0x79f28b79, 0xe4d337e4, 0x9531a495, 0x9139a891,
     0x66ccaa66, 0xb571c4b5, 0x3e7c423e, 0x70e09070, 0x0e1c120e, 0xf6f701f6, 0x03060503, 0x4890d848, 0xb969d0b9, 0x57aef957, 0x356a5f35, 0x61c2a361, 0x9e27b99e, 0x1d3a271d, 0xc19958c1, 0x86179186,
     0x2e5c722e, 0x254a6f25, 0x78f08878, 0xba6fd5ba, 0xc69751c6, 0xb473c7b4, 0xa657f1a6, 0x1c38241c, 0x1f3e211f, 0x74e89c74, 0xdda17cdd, 0xe8cb23e8, 0x8a0f858a, 0x8b0d868b, 0xbd61dcbd, 0x4b96dd4b,
     0x0d1a170d, 0x89098089, 0xa159f8a1, 0x8c038f8c, 0x68d0b868, 0x4284c642, 0xe6d731e6, 0xbf65dabf, 0x0f1e110f, 0x2d5a772d, 0x9929b099, 0x4182c341, 0x162c3a16, 0xbb6dd6bb, 0x54a8fc54, 0xb07bcbb0,
     0x11223311, 0x982bb398, 0xf8eb13f8, 0xe1d938e1, 0x9433a794, 0x8e07898e, 0xd9a970d9, 0x69d2bb69, 0xe9c920e9, 0x87159287, 0x1e3c221e, 0x9b2db69b, 0xdfa57adf, 0x28507828, 0x55aaff55, 0xce8749ce,
     0x7dfa877d, 0xc98940c9, 0x821f9d82, 0xca8f45ca, 0xf0fb0bf0, 0x478ec947, 0x59b2eb59, 0xfaef15fa, 0xaf45eaaf, 0xa25ffda2, 0xd4b367d4, 0xad41ecad, 0xc09b5bc0, 0x72e49672, 0xa453f7a4, 0x9c23bf9c,
     0x7bf68d7b, 0x77ee9977, 0x7cf8847c, 0x63c6a563, 0xc59154c5, 0x6fdeb16f, 0x6bd6bd6b, 0xf2ff0df2, 0x2b567d2b, 0x67cea967, 0x01020301, 0x30605030, 0x76ec9a76, 0xab4de6ab, 0xd7b562d7, 0xfee719fe,
     0xc39d5ec3, 0x23466523, 0xc79552c7, 0x04080c04, 0x9a2fb59a, 0x050a0f05, 0x9637a196, 0x18302818, 0xe2df3de2, 0x801b9b80, 0x12243612, 0x070e0907, 0x75ea9f75, 0xb27fcdb2, 0x274e6927, 0xebcd26eb,
     0x264c6a26, 0x933dae93, 0xfde11cfd, 0xb775c2b7, 0xcc834fcc, 0xf7f502f7, 0x3f7e413f, 0x366c5a36, 0xf1f908f1, 0xe5d134e5, 0xa551f4a5, 0x34685c34, 0x152a3f15, 0x31625331, 0xd8ab73d8, 0x71e29371,
     0xedc12ced, 0x00000000, 0xd1b968d1, 0x53a6f553, 0x5bb6ed5b, 0xb179c8b1, 0xfce31ffc, 0x20406020, 0x39724b39, 0xbe67d9be, 0xcb8d46cb, 0x6ad4be6a, 0xcf854acf, 0x58b0e858, 0x4c98d44c, 0x4a94de4a,
     0x1a342e1a, 0x2c58742c, 0x831d9e83, 0x09121b09, 0xa05bfba0, 0x5ab4ee5a, 0x6edcb26e, 0x1b362d1b, 0xb37dceb3, 0xd6b761d6, 0x3b764d3b, 0x52a4f652, 0x84139784, 0x2f5e712f, 0xe3dd3ee3, 0x29527b29,
     0x8f058a8f, 0x4080c040, 0xa35dfea3, 0x51a2f351, 0xf5f104f5, 0x38704838, 0x9d21bc9d, 0x923fad92, 0x21426321, 0xdaaf75da, 0xb677c1b6, 0xbc63dfbc, 0xd2bf6dd2, 0xf3fd0ef3, 0xffe51aff, 0x10203010,
     0xfbed16fb, 0xaa4fe5aa, 0xefc52aef, 0xd0bb6bd0, 0x85119485, 0x33665533, 0x4d9ad74d, 0x4386c543, 0x7ffe817f, 0x02040602, 0xf9e910f9, 0x458acf45, 0xa84be3a8, 0x9f25ba9f, 0x3c78443c, 0x50a0f050
 ],
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     0x2db69b9b, 0x3c221e1e, 0x15928787, 0xc920e9e9, 0x8749cece, 0xaaff5555, 0x50782828, 0xa57adfdf, 0xd938e1e1, 0xeb13f8f8, 0x2bb39898, 0x22331111, 0xd2bb6969, 0xa970d9d9, 0x07898e8e, 0x33a79494,
     0x82c34141, 0x29b09999, 0x5a772d2d, 0x1e110f0f, 0x7bcbb0b0, 0xa8fc5454, 0x6dd6bbbb, 0x2c3a1616, 0x038f8c8c, 0x59f8a1a1, 0x09808989, 0x1a170d0d, 0x65dabfbf, 0xd731e6e6, 0x84c64242, 0xd0b86868,
     0xcb23e8e8, 0xa17cdddd, 0xe89c7474, 0x3e211f1f, 0x96dd4b4b, 0x61dcbdbd, 0x0d868b8b, 0x0f858a8a, 0x6fd5baba, 0xf0887878, 0x4a6f2525, 0x5c722e2e, 0x38241c1c, 0x57f1a6a6, 0x73c7b4b4, 0x9751c6c6,
     0xc2a36161, 0x6a5f3535, 0xaef95757, 0x69d0b9b9, 0x17918686, 0x9958c1c1, 0x3a271d1d, 0x27b99e9e, 0xe0907070, 0x7c423e3e, 0x71c4b5b5, 0xccaa6666, 0x90d84848, 0x06050303, 0xf701f6f6, 0x1c120e0e,
     0x9f5dc2c2, 0xbd6ed3d3, 0x43efacac, 0xc4a66262, 0x39a89191, 0x31a49595, 0xd337e4e4, 0xf28b7979, 0xdb3be0e0, 0x64563232, 0x744e3a3a, 0x141e0a0a, 0x92db4949, 0x0c0a0606, 0x486c2424, 0xb8e45c5c,
     0xd8b46c6c, 0xacfa5656, 0xf307f4f4, 0xcf25eaea, 0xcaaf6565, 0xf48e7a7a, 0x47e9aeae, 0x10180808, 0xd532e7e7, 0x8b43c8c8, 0x6e593737, 0xdab76d6d, 0x018c8d8d, 0xb164d5d5, 0x9cd24e4e, 0x49e0a9a9,
     0x9357c4c4, 0x55f2a7a7, 0xfc827e7e, 0x7a473d3d, 0xc8ac6464, 0xbae75d5d, 0x322b1919, 0xe6957373, 0x814ccdcd, 0x18140c0c, 0x26351313, 0xc32fecec, 0xbee15f5f, 0x35a29797, 0x88cc4444, 0x2e391717,
     0x8cca4646, 0xc729eeee, 0x6bd3b8b8, 0x283c1414, 0xa779dede, 0xbce25e5e, 0x161d0b0b, 0xad76dbdb, 0xc0a06060, 0x19988181, 0x9ed14f4f, 0xa37fdcdc, 0x44662222, 0x547e2a2a, 0x3bab9090, 0x0b838888,
     0x8acf4545, 0xe910f9f9, 0x04060202, 0xfe817f7f, 0xa0f05050, 0x78443c3c, 0x25ba9f9f, 0x4be3a8a8, 0xbb6bd0d0, 0xc52aefef, 0x4fe5aaaa, 0xed16fbfb, 0x86c54343, 0x9ad74d4d, 0x66553333, 0x11948585,
     0x63dfbcbc, 0x77c1b6b6, 0xaf75dada, 0x42632121, 0x20301010, 0xe51affff, 0xfd0ef3f3, 0xbf6dd2d2, 0xa2f35151, 0x5dfea3a3, 0x80c04040, 0x058a8f8f, 0x3fad9292, 0x21bc9d9d, 0x70483838, 0xf104f5f5,
     0xa4f65252, 0x764d3b3b, 0xb761d6d6, 0x7dceb3b3, 0x527b2929, 0xdd3ee3e3, 0x5e712f2f, 0x13978484, 0x121b0909, 0x1d9e8383, 0x58742c2c, 0x342e1a1a, 0x362d1b1b, 0xdcb26e6e, 0xb4ee5a5a, 0x5bfba0a0,
     0xd4be6a6a, 0x8d46cbcb, 0x67d9bebe, 0x724b3939, 0x94de4a4a, 0x98d44c4c, 0xb0e85858, 0x854acfcf, 0xa6f55353, 0xb968d1d1, 0x00000000, 0xc12ceded, 0x40602020, 0xe31ffcfc, 0x79c8b1b1, 0xb6ed5b5b,
     0x685c3434, 0x51f4a5a5, 0xd134e5e5, 0xf908f1f1, 0xe2937171, 0xab73d8d8, 0x62533131, 0x2a3f1515, 0x75c2b7b7, 0xe11cfdfd, 0x3dae9393, 0x4c6a2626, 0x6c5a3636, 0x7e413f3f, 0xf502f7f7, 0x834fcccc,
     0x0e090707, 0x24361212, 0x1b9b8080, 0xdf3de2e2, 0xcd26ebeb, 0x4e692727, 0x7fcdb2b2, 0xea9f7575, 0x080c0404, 0x9552c7c7, 0x46652323, 0x9d5ec3c3, 0x30281818, 0x37a19696, 0x0a0f0505, 0x2fb59a9a,
     0x60503030, 0x02030101, 0xcea96767, 0x567d2b2b, 0xe719fefe, 0xb562d7d7, 0x4de6abab, 0xec9a7676, 0xc6a56363, 0xf8847c7c, 0xee997777, 0xf68d7b7b, 0xff0df2f2, 0xd6bd6b6b, 0xdeb16f6f, 0x9154c5c5,
     0x41ecadad, 0xb367d4d4, 0x5ffda2a2, 0x45eaafaf, 0x23bf9c9c, 0x53f7a4a4, 0xe4967272, 0x9b5bc0c0, 0x8f45caca, 0x1f9d8282, 0x8940c9c9, 0xfa877d7d, 0xef15fafa, 0xb2eb5959, 0x8ec94747, 0xfb0bf0f0
 ],
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     0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0x30101020, 0x1affffe5, 0x0ef3f3fd, 0x6dd2d2bf, 0xf35151a2, 0xfea3a35d, 0xc0404080, 0x8a8f8f05, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x04f5f5f1,
     0xcf45458a, 0x10f9f9e9, 0x06020204, 0x817f7ffe, 0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed, 0xc5434386, 0xd74d4d9a, 0x55333366, 0x94858511,
     0xbe6a6ad4, 0x46cbcb8d, 0xd9bebe67, 0x4b393972, 0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, 0xf55353a6, 0x68d1d1b9, 0x00000000, 0x2cededc1, 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6,
     0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x7b292952, 0x3ee3e3dd, 0x712f2f5e, 0x97848413, 0x1b090912, 0x9e83831d, 0x742c2c58, 0x2e1a1a34, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b,
     0x0907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, 0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x0c040408, 0x52c7c795, 0x65232346, 0x5ec3c39d, 0x28181830, 0xa1969637, 0x0f05050a, 0xb59a9a2f,
     0x5c343468, 0xf4a5a551, 0x34e5e5d1, 0x08f1f1f9, 0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c, 0x5a36366c, 0x413f3f7e, 0x02f7f7f5, 0x4fcccc83,
     0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0xbf9c9c23, 0xf7a4a453, 0x967272e4, 0x5bc0c09b, 0x45caca8f, 0x9d82821f, 0x40c9c989, 0x877d7dfa, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0x0bf0f0fb,
     0x50303060, 0x03010102, 0xa96767ce, 0x7d2b2b56, 0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6, 0x0df2f2ff, 0xbd6b6bd6, 0xb16f6fde, 0x54c5c591,
     0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, 0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c, 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a, 0xdabfbf65, 0x31e6e6d7, 0xc6424284, 0xb86868d0,
     0xb69b9b2d, 0x221e1e3c, 0x92878715, 0x20e9e9c9, 0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122, 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433,
     0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0x91868617, 0x58c1c199, 0x271d1d3a, 0xb99e9e27, 0x907070e0, 0x423e3e7c, 0xc4b5b571, 0xaa6666cc, 0xd8484890, 0x05030306, 0x01f6f6f7, 0x120e0e1c,
     0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, 0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c, 0x241c1c38, 0xf1a6a657, 0xc7b4b473, 0x51c6c697,
     0xb46c6cd8, 0xfa5656ac, 0x07f4f4f3, 0x25eaeacf, 0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda, 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949,
     0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xa8919139, 0xa4959531, 0x37e4e4d3, 0x8b7979f2, 0x3be0e0db, 0x56323264, 0x4e3a3a74, 0x1e0a0a14, 0xdb494992, 0x0a06060c, 0x6c242448, 0xe45c5cb8,
     0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, 0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3, 0x66222244, 0x7e2a2a54, 0xab90903b, 0x8388880b,
     0x57c4c493, 0xf2a7a755, 0x827e7efc, 0x473d3d7a, 0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3, 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e
 ],
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     0x3434685c, 0xa5a551f4, 0xe5e5d134, 0xf1f1f908, 0x7171e293, 0xd8d8ab73, 0x31316253, 0x15152a3f, 0xb7b775c2, 0xfdfde11c, 0x93933dae, 0x26264c6a, 0x36366c5a, 0x3f3f7e41, 0xf7f7f502, 0xcccc834f,
     0x07070e09, 0x12122436, 0x80801b9b, 0xe2e2df3d, 0xebebcd26, 0x27274e69, 0xb2b27fcd, 0x7575ea9f, 0x0404080c, 0xc7c79552, 0x23234665, 0xc3c39d5e, 0x18183028, 0x969637a1, 0x05050a0f, 0x9a9a2fb5,
     0x30306050, 0x01010203, 0x6767cea9, 0x2b2b567d, 0xfefee719, 0xd7d7b562, 0xabab4de6, 0x7676ec9a, 0x6363c6a5, 0x7c7cf884, 0x7777ee99, 0x7b7bf68d, 0xf2f2ff0d, 0x6b6bd6bd, 0x6f6fdeb1, 0xc5c59154,
     0xadad41ec, 0xd4d4b367, 0xa2a25ffd, 0xafaf45ea, 0x9c9c23bf, 0xa4a453f7, 0x7272e496, 0xc0c09b5b, 0xcaca8f45, 0x82821f9d, 0xc9c98940, 0x7d7dfa87, 0xfafaef15, 0x5959b2eb, 0x47478ec9, 0xf0f0fb0b,
     0x45458acf, 0xf9f9e910, 0x02020406, 0x7f7ffe81, 0x5050a0f0, 0x3c3c7844, 0x9f9f25ba, 0xa8a84be3, 0xd0d0bb6b, 0xefefc52a, 0xaaaa4fe5, 0xfbfbed16, 0x434386c5, 0x4d4d9ad7, 0x33336655, 0x85851194,
     0xbcbc63df, 0xb6b677c1, 0xdadaaf75, 0x21214263, 0x10102030, 0xffffe51a, 0xf3f3fd0e, 0xd2d2bf6d, 0x5151a2f3, 0xa3a35dfe, 0x404080c0, 0x8f8f058a, 0x92923fad, 0x9d9d21bc, 0x38387048, 0xf5f5f104,
     0x5252a4f6, 0x3b3b764d, 0xd6d6b761, 0xb3b37dce, 0x2929527b, 0xe3e3dd3e, 0x2f2f5e71, 0x84841397, 0x0909121b, 0x83831d9e, 0x2c2c5874, 0x1a1a342e, 0x1b1b362d, 0x6e6edcb2, 0x5a5ab4ee, 0xa0a05bfb,
     0x6a6ad4be, 0xcbcb8d46, 0xbebe67d9, 0x3939724b, 0x4a4a94de, 0x4c4c98d4, 0x5858b0e8, 0xcfcf854a, 0x5353a6f5, 0xd1d1b968, 0x00000000, 0xededc12c, 0x20204060, 0xfcfce31f, 0xb1b179c8, 0x5b5bb6ed,
     0xc2c29f5d, 0xd3d3bd6e, 0xacac43ef, 0x6262c4a6, 0x919139a8, 0x959531a4, 0xe4e4d337, 0x7979f28b, 0xe0e0db3b, 0x32326456, 0x3a3a744e, 0x0a0a141e, 0x494992db, 0x06060c0a, 0x2424486c, 0x5c5cb8e4,
     0x6c6cd8b4, 0x5656acfa, 0xf4f4f307, 0xeaeacf25, 0x6565caaf, 0x7a7af48e, 0xaeae47e9, 0x08081018, 0xe7e7d532, 0xc8c88b43, 0x37376e59, 0x6d6ddab7, 0x8d8d018c, 0xd5d5b164, 0x4e4e9cd2, 0xa9a949e0,
     0xc4c49357, 0xa7a755f2, 0x7e7efc82, 0x3d3d7a47, 0x6464c8ac, 0x5d5dbae7, 0x1919322b, 0x7373e695, 0xcdcd814c, 0x0c0c1814, 0x13132635, 0xececc32f, 0x5f5fbee1, 0x979735a2, 0x444488cc, 0x17172e39,
     0x46468cca, 0xeeeec729, 0xb8b86bd3, 0x1414283c, 0xdedea779, 0x5e5ebce2, 0x0b0b161d, 0xdbdbad76, 0x6060c0a0, 0x81811998, 0x4f4f9ed1, 0xdcdca37f, 0x22224466, 0x2a2a547e, 0x90903bab, 0x88880b83,
     0x9b9b2db6, 0x1e1e3c22, 0x87871592, 0xe9e9c920, 0xcece8749, 0x5555aaff, 0x28285078, 0xdfdfa57a, 0xe1e1d938, 0xf8f8eb13, 0x98982bb3, 0x11112233, 0x6969d2bb, 0xd9d9a970, 0x8e8e0789, 0x949433a7,
     0x414182c3, 0x999929b0, 0x2d2d5a77, 0x0f0f1e11, 0xb0b07bcb, 0x5454a8fc, 0xbbbb6dd6, 0x16162c3a, 0x8c8c038f, 0xa1a159f8, 0x89890980, 0x0d0d1a17, 0xbfbf65da, 0xe6e6d731, 0x424284c6, 0x6868d0b8,
     0xe8e8cb23, 0xdddda17c, 0x7474e89c, 0x1f1f3e21, 0x4b4b96dd, 0xbdbd61dc, 0x8b8b0d86, 0x8a8a0f85, 0xbaba6fd5, 0x7878f088, 0x25254a6f, 0x2e2e5c72, 0x1c1c3824, 0xa6a657f1, 0xb4b473c7, 0xc6c69751,
     0x6161c2a3, 0x35356a5f, 0x5757aef9, 0xb9b969d0, 0x86861791, 0xc1c19958, 0x1d1d3a27, 0x9e9e27b9, 0x7070e090, 0x3e3e7c42, 0xb5b571c4, 0x6666ccaa, 0x484890d8, 0x03030605, 0xf6f6f701, 0x0e0e1c12
 ],
 [
     0x9735a297, 0x5fbee15f, 0x172e3917, 0x4488cc44, 0x0c18140c, 0xcd814ccd, 0xecc32fec, 0x13263513, 0x5dbae75d, 0x64c8ac64, 0x73e69573, 0x19322b19, 0xa755f2a7, 0xc49357c4, 0x3d7a473d, 0x7efc827e,
     0x2a547e2a, 0x22446622, 0x880b8388, 0x903bab90, 0x81199881, 0x60c0a060, 0xdca37fdc, 0x4f9ed14f, 0x5ebce25e, 0xdea779de, 0xdbad76db, 0x0b161d0b, 0xeec729ee, 0x468cca46, 0x14283c14, 0xb86bd3b8,
     0x060c0a06, 0x4992db49, 0x5cb8e45c, 0x24486c24, 0x32645632, 0xe0db3be0, 0x0a141e0a, 0x3a744e3a, 0x9531a495, 0x9139a891, 0x79f28b79, 0xe4d337e4, 0xd3bd6ed3, 0xc29f5dc2, 0x62c4a662, 0xac43efac,
     0xd5b164d5, 0x8d018c8d, 0xa949e0a9, 0x4e9cd24e, 0xc88b43c8, 0xe7d532e7, 0x6ddab76d, 0x376e5937, 0x7af48e7a, 0x65caaf65, 0x08101808, 0xae47e9ae, 0x56acfa56, 0x6cd8b46c, 0xeacf25ea, 0xf4f307f4,
     0xa657f1a6, 0x1c38241c, 0xc69751c6, 0xb473c7b4, 0x78f08878, 0xba6fd5ba, 0x2e5c722e, 0x254a6f25, 0xbd61dcbd, 0x4b96dd4b, 0x8a0f858a, 0x8b0d868b, 0xdda17cdd, 0xe8cb23e8, 0x1f3e211f, 0x74e89c74,
     0x03060503, 0x4890d848, 0x0e1c120e, 0xf6f701f6, 0x3e7c423e, 0x70e09070, 0x66ccaa66, 0xb571c4b5, 0xc19958c1, 0x86179186, 0x9e27b99e, 0x1d3a271d, 0x356a5f35, 0x61c2a361, 0xb969d0b9, 0x57aef957,
     0xd9a970d9, 0x69d2bb69, 0x9433a794, 0x8e07898e, 0xf8eb13f8, 0xe1d938e1, 0x11223311, 0x982bb398, 0x55aaff55, 0xce8749ce, 0xdfa57adf, 0x28507828, 0x1e3c221e, 0x9b2db69b, 0xe9c920e9, 0x87159287,
     0xe6d731e6, 0xbf65dabf, 0x68d0b868, 0x4284c642, 0xa159f8a1, 0x8c038f8c, 0x0d1a170d, 0x89098089, 0x54a8fc54, 0xb07bcbb0, 0x162c3a16, 0xbb6dd6bb, 0x9929b099, 0x4182c341, 0x0f1e110f, 0x2d5a772d,
     0x6bd6bd6b, 0xf2ff0df2, 0xc59154c5, 0x6fdeb16f, 0x7cf8847c, 0x63c6a563, 0x7bf68d7b, 0x77ee9977, 0xd7b562d7, 0xfee719fe, 0x76ec9a76, 0xab4de6ab, 0x01020301, 0x30605030, 0x2b567d2b, 0x67cea967,
     0x59b2eb59, 0xfaef15fa, 0xf0fb0bf0, 0x478ec947, 0x821f9d82, 0xca8f45ca, 0x7dfa877d, 0xc98940c9, 0xa453f7a4, 0x9c23bf9c, 0xc09b5bc0, 0x72e49672, 0xd4b367d4, 0xad41ecad, 0xaf45eaaf, 0xa25ffda2,
     0x3f7e413f, 0x366c5a36, 0xcc834fcc, 0xf7f502f7, 0xfde11cfd, 0xb775c2b7, 0x264c6a26, 0x933dae93, 0xd8ab73d8, 0x71e29371, 0x152a3f15, 0x31625331, 0xa551f4a5, 0x34685c34, 0xf1f908f1, 0xe5d134e5,
     0x9637a196, 0x18302818, 0x9a2fb59a, 0x050a0f05, 0xc79552c7, 0x04080c04, 0xc39d5ec3, 0x23466523, 0x274e6927, 0xebcd26eb, 0x75ea9f75, 0xb27fcdb2, 0x12243612, 0x070e0907, 0xe2df3de2, 0x801b9b80,
     0x6edcb26e, 0x1b362d1b, 0xa05bfba0, 0x5ab4ee5a, 0x831d9e83, 0x09121b09, 0x1a342e1a, 0x2c58742c, 0xe3dd3ee3, 0x29527b29, 0x84139784, 0x2f5e712f, 0x3b764d3b, 0x52a4f652, 0xb37dceb3, 0xd6b761d6,
     0xfce31ffc, 0x20406020, 0x5bb6ed5b, 0xb179c8b1, 0xd1b968d1, 0x53a6f553, 0xedc12ced, 0x00000000, 0x4c98d44c, 0x4a94de4a, 0xcf854acf, 0x58b0e858, 0xcb8d46cb, 0x6ad4be6a, 0x39724b39, 0xbe67d9be,
     0x4d9ad74d, 0x4386c543, 0x85119485, 0x33665533, 0xefc52aef, 0xd0bb6bd0, 0xfbed16fb, 0xaa4fe5aa, 0x3c78443c, 0x50a0f050, 0xa84be3a8, 0x9f25ba9f, 0xf9e910f9, 0x458acf45, 0x7ffe817f, 0x02040602,
     0x9d21bc9d, 0x923fad92, 0xf5f104f5, 0x38704838, 0xa35dfea3, 0x51a2f351, 0x8f058a8f, 0x4080c040, 0xffe51aff, 0x10203010, 0xd2bf6dd2, 0xf3fd0ef3, 0xb677c1b6, 0xbc63dfbc, 0x21426321, 0xdaaf75da
 ],
 [
     0x3e211f1f, 0xe89c7474, 0xa17cdddd, 0xcb23e8e8, 0x0f858a8a, 0x0d868b8b, 0x61dcbdbd, 0x96dd4b4b, 0x5c722e2e, 0x4a6f2525, 0xf0887878, 0x6fd5baba, 0x9751c6c6, 0x73c7b4b4, 0x57f1a6a6, 0x38241c1c,
     0x69d0b9b9, 0xaef95757, 0x6a5f3535, 0xc2a36161, 0x27b99e9e, 0x3a271d1d, 0x9958c1c1, 0x17918686, 0xccaa6666, 0x71c4b5b5, 0x7c423e3e, 0xe0907070, 0x1c120e0e, 0xf701f6f6, 0x06050303, 0x90d84848,
     0xc920e9e9, 0x15928787, 0x3c221e1e, 0x2db69b9b, 0xa57adfdf, 0x50782828, 0xaaff5555, 0x8749cece, 0x22331111, 0x2bb39898, 0xeb13f8f8, 0xd938e1e1, 0x33a79494, 0x07898e8e, 0xa970d9d9, 0xd2bb6969,
     0x1e110f0f, 0x5a772d2d, 0x29b09999, 0x82c34141, 0x2c3a1616, 0x6dd6bbbb, 0xa8fc5454, 0x7bcbb0b0, 0x1a170d0d, 0x09808989, 0x59f8a1a1, 0x038f8c8c, 0xd0b86868, 0x84c64242, 0xd731e6e6, 0x65dabfbf,
     0x7a473d3d, 0xfc827e7e, 0x55f2a7a7, 0x9357c4c4, 0xe6957373, 0x322b1919, 0xbae75d5d, 0xc8ac6464, 0xc32fecec, 0x26351313, 0x18140c0c, 0x814ccdcd, 0x2e391717, 0x88cc4444, 0x35a29797, 0xbee15f5f,
     0x283c1414, 0x6bd3b8b8, 0xc729eeee, 0x8cca4646, 0xad76dbdb, 0x161d0b0b, 0xbce25e5e, 0xa779dede, 0xa37fdcdc, 0x9ed14f4f, 0x19988181, 0xc0a06060, 0x0b838888, 0x3bab9090, 0x547e2a2a, 0x44662222,
     0xc4a66262, 0x43efacac, 0xbd6ed3d3, 0x9f5dc2c2, 0xf28b7979, 0xd337e4e4, 0x31a49595, 0x39a89191, 0x141e0a0a, 0x744e3a3a, 0x64563232, 0xdb3be0e0, 0xb8e45c5c, 0x486c2424, 0x0c0a0606, 0x92db4949,
     0xcf25eaea, 0xf307f4f4, 0xacfa5656, 0xd8b46c6c, 0x10180808, 0x47e9aeae, 0xf48e7a7a, 0xcaaf6565, 0xdab76d6d, 0x6e593737, 0x8b43c8c8, 0xd532e7e7, 0x49e0a9a9, 0x9cd24e4e, 0xb164d5d5, 0x018c8d8d,
     0x7dceb3b3, 0xb761d6d6, 0x764d3b3b, 0xa4f65252, 0x13978484, 0x5e712f2f, 0xdd3ee3e3, 0x527b2929, 0x342e1a1a, 0x58742c2c, 0x1d9e8383, 0x121b0909, 0x5bfba0a0, 0xb4ee5a5a, 0xdcb26e6e, 0x362d1b1b,
     0x724b3939, 0x67d9bebe, 0x8d46cbcb, 0xd4be6a6a, 0x854acfcf, 0xb0e85858, 0x98d44c4c, 0x94de4a4a, 0xc12ceded, 0x00000000, 0xb968d1d1, 0xa6f55353, 0xb6ed5b5b, 0x79c8b1b1, 0xe31ffcfc, 0x40602020,
     0xfe817f7f, 0x04060202, 0xe910f9f9, 0x8acf4545, 0x4be3a8a8, 0x25ba9f9f, 0x78443c3c, 0xa0f05050, 0xed16fbfb, 0x4fe5aaaa, 0xc52aefef, 0xbb6bd0d0, 0x11948585, 0x66553333, 0x9ad74d4d, 0x86c54343,
     0x42632121, 0xaf75dada, 0x77c1b6b6, 0x63dfbcbc, 0xbf6dd2d2, 0xfd0ef3f3, 0xe51affff, 0x20301010, 0x058a8f8f, 0x80c04040, 0x5dfea3a3, 0xa2f35151, 0xf104f5f5, 0x70483838, 0x21bc9d9d, 0x3fad9292,
     0x567d2b2b, 0xcea96767, 0x02030101, 0x60503030, 0xec9a7676, 0x4de6abab, 0xb562d7d7, 0xe719fefe, 0xf68d7b7b, 0xee997777, 0xf8847c7c, 0xc6a56363, 0x9154c5c5, 0xdeb16f6f, 0xd6bd6b6b, 0xff0df2f2,
     0x45eaafaf, 0x5ffda2a2, 0xb367d4d4, 0x41ecadad, 0x9b5bc0c0, 0xe4967272, 0x53f7a4a4, 0x23bf9c9c, 0xfa877d7d, 0x8940c9c9, 0x1f9d8282, 0x8f45caca, 0xfb0bf0f0, 0x8ec94747, 0xb2eb5959, 0xef15fafa,
     0xf908f1f1, 0xd134e5e5, 0x51f4a5a5, 0x685c3434, 0x2a3f1515, 0x62533131, 0xab73d8d8, 0xe2937171, 0x4c6a2626, 0x3dae9393, 0xe11cfdfd, 0x75c2b7b7, 0x834fcccc, 0xf502f7f7, 0x7e413f3f, 0x6c5a3636,
     0xdf3de2e2, 0x1b9b8080, 0x24361212, 0x0e090707, 0xea9f7575, 0x7fcdb2b2, 0x4e692727, 0xcd26ebeb, 0x9d5ec3c3, 0x46652323, 0x9552c7c7, 0x080c0404, 0x2fb59a9a, 0x0a0f0505, 0x37a19696, 0x30281818
 ]
]

secretKey = [0 for _ in range(16)]
MixColumnLUT = [[0 for col in range(256)] for row in range(4)]

for i in range(0,4):
 for j in range(0,256):
  t = [0 for _ in range(4)]
  t[3] = format(gmul[matrix_4x4[i + 0]][j],'02x')
  t[2]=  format(gmul[matrix_4x4[i + 4]][j],'02x')
  t[1] = format(gmul[matrix_4x4[i + 8]][j],'02x')
  t[0] = format(gmul[matrix_4x4[i + 12]][j],'02x')
  x = "".join(x for x in t)
  MixColumnLUT[i][j]=x

for i in range(0,16):
 M_TBoxesKey= format(M_TBoxesR0[i][0],'08x')
 for j in range(0,256):
  keyOffset = Sbox[j]
  gussedKey = MixColumnLUT[i % 4][keyOffset]
  if (M_TBoxesKey==gussedKey):
   secretKey[i]=j

"""  
    ḱ is the result of applying ShiftRows to the round key 
    Therefore, To get the secretKey you need to unShiftRow.

    unShiftRows
    +----+----+----+----+  
    | 00 | 04 | 08 | 12 |
    +----+----+----+----+
    | 01 | 05 | 09 | 13 | 
    +----+----+----+----+ 
    | 02 | 06 | 10 | 14 |
    +----+----+----+----+
    | 03 | 07 | 11 | 15 |
    +----+----+----+----+
"""
for i in range(1,4):
 s=0
 while(s<i):
  tmp = secretKey[i+12]
  for k in range(2,-1,-1):
   secretKey[k*4+i+4]=secretKey[k*4+i]
  secretKey[i]=tmp
  s=s+1

secretKey = "".join(hex(x)[2:] for x in secretKey)
print "secretKey:"+ secretKey.upper()
secretKey = binascii.unhexlify(secretKey)

#decrypt Flag and print
flag = base64.b64decode(encFlag)
cipher = AES.new(secretKey, AES.MODE_ECB)
flag = cipher.decrypt(flag)
print "deryptedFlag:"+ flag


h2spices-MacBook-Pro:Seccon2016_Crypto500_OAES h2spice$ python exploit_Crypto500.py
encryptedFlag:g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc=
secretKey:6C2893F21B6185E8567238CB78184945
deryptedFlag:SECCON{owSkwPeH1CHQdPV9KWrSmz9n}

Thank you!

SECCON 2016 Online CTF - Binary/Crypto500 Obfuscated AES Write up (Japanese)



Hello, h2spiceです。
SECCON2016 Online CTF-Binary/Crypto500 Obfuscated AESのWrite upです。
今年は昨年とは違ってService上の脆弱性に対するExploitに焦点を当てるよりはSoftware ProtectionとしていくつかのMitigation Techniqueに焦点を合わせました。
White-box AESを実装し、LLVM、難読化を適用しました。
個人的には様々な方法で解けることを期待していたが、意外に一つのチームしか解く事ができなくました。
Thanks, PPP ...
時間が十分あったならば、多くのPlayerが解くことができた問題だと思います。
APKは下記のリンクでダウンロードすることができます。 知りたい点があったらいつでも連絡ください。
OAES.zip [Download]

White-box AESに対する十分な理解なしにも解決できる方法はいくつかあると思いますが、
本Write-upは、原始Chow et al.'s White-box AES scheme (https://www.cs.colorado.edu/~jrblack/class/csci7000/s03/project/oorschot-whitebox.pdf)に対する攻撃に焦点を合わせて作成しました。

Obfuscated AESはencrypted Flagを出力するAndroid Applicationです。
Applicationの中に隠されたsecretKeyを探してencryptedFlagを復号化すると、Flagを得ることができます。

.apkをdecompileすると、以下のようなコードを得ることができます。

実行の流れは下記の通りです。
  1. 0~3600の間の任意の値を生成して、この値をindexで使用する。
  2. array.xmlに定義されたtable(encryptedFlag)[index]の値encryptedFlagに保存する。
    (e.g.,
              <?xml version="1.0" encoding="utf-8"?>
              <resources>
                  <string-array name="tables">
                      <item>g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc=</item>
                      <item>T6i4c4TH+b1yQGKaMdkyzeCErYVHVxtsY1Zw45MJzjM=</item>
                      <item>hPhT8kZaCwlrtgo6Fq6t2e8PuIaQUxoMbqRP0n8nZ14=</item>
                      <item>uGI3zyZ6PrP9ouZg7kp4Gc4rexZxssoYxk9geUeIs54=</item>
                      ....
    array.xmlに定義されたencryptedFlagはFlag(plain)を同じsecretKeyにN(index+1)稼いだ暗号化されたCiphertextです。 
  3. encryptedFlag出力する
  4. native-liv.soのfunction.a(encryption function)とencryptedFlagを暗号化する。
  5. 3.4を繰り返す。

Native Function.aのPseudo code(IDA Hex-Rays Decompiler)下記の通りです。
int __cdecl Java_kr_repo_h2spice_crypto500_MainActivity_a(int a1, int a2, int input)
{
  // [COLLAPSED LOCAL DECLARATIONS. PRESS KEYPAD CTRL-"+" TO EXPAND]
  v31 = *MK_FP(__GS__, 20);
  input_base64 = (*(*a1 + 676))(a1, input, 0);
  *output_base64_16 = 0LL;
  *output_base64_0 = 0LL;
  v30 = 0;
  DENCPKY6hzMem3SuzgIXu4u6vxbF1sajPOJ75aN2VTdc7SCL(output_base64, input_base64);
  // base64Decode
  *cipherText_16 = 0LL;
  *cipherText_0 = 0LL;
  TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq(output_base64, cipherText);
  // encryption 16bytes
  TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq(output_base64+16, cipherText+16);
  // encryption 16bytes
  
  *base64_out_final = 0LL;
  APtMDGO79Go3cbIkFca2rN0KszanZXOZ7dIPsxDBletW5gdo(base64_out_final, cipherText, 32);// base64Encode
  ...

実行の流れは下記の通りです。
  1. Java로 부터 전달받은 input data(base64 encoded)를 base64 Decoding한다.
    (base64decode funciton : DENCPKY6hzMem3SuzgIXu4u6vxbF1sajPOJ75aN2VTdc7SCL)
  2. 16byte block씩 암호화한다.
    (encryption function : TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq)
  3. 암호화된 Data(32bytes)를 base64 Encoding한다.
    (base64encode function : APtMDGO79Go3cbIkFca2rN0KszanZXOZ7dIPsxDBletW5gdo)

encryption function(TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq)を分析して暗号化に使用されるsecret-keyを見つけることが問題の核心です。
しかし、難読化されていて複雑です。 (しかし、十分に分析可能な程度の難読化と思います。)


OAESに実装されたWhite-box AESについて理論的に簡単に説明します。
もちろんWhite-box AESの理論がなくても解決できる方法はたくさんあると思います。

Conventional AES Schemeは以下のような形に変形されことができます。
  1. The for-loop can be redefined to bring the transformation AddRoundKey(state, k0) inside it while pushing AddRoundKey(state, k9) out.
  2. Since SubBytes applies the same S-box to each byte of the state, SubBytes followed by ShiftRows gives the same result as ShiftRows followed by SubBytes.
  3. Since ShiftRows is a linear transformation (recall that it is a permutation),AddRoundKey(state, kr−1) followed by ShiftRows(state) gives the same result as ShiftRows(state) followed by AddRoundKey(state, ḱr−1); here, ḱr−1 is the result of applying ShiftRows to the round key kr−1.
ChowのWhite-box AES Schemeは基本的にTable(T-boxes)基盤です。 そしてAddRoundKey、SubBytesのtransformationは結合されことができます。 e.g., SubBytes(AddRoundKey(state,kr))
各Round(1-10)のpre-computed KeyTable、T-boxes:SubBytes(AddRoundKey(state、ḱr))を生成し、このT-boxesベースに暗号化を実行することができます。

T-boxesは以下の数式で生成されます。

つまり、Round1のT-boxesは以下のように生成されことができます。



char TboxesRound1[16][256] = 
{       
    /*Round0 ḱ[0] is 0x6c*/
    {
        0x50, 0x3c, 0x9f, 0xa8, 0x45, 0xf9, 0x02, 0x7f, 0x43, 0x4d, 0x33, 0x85, 0xd0, 0xef, 0xaa, 0xfb,
        0x10, 0xff, 0xf3, 0xd2, 0xbc, 0xb6, 0xda, 0x21, 0x92, 0x9d, 0x38, 0xf5, 0x51, 0xa3, 0x40, 0x8f,
        0x29, 0xe3, 0x2f, 0x84, 0x52, 0x3b, 0xd6, 0xb3, 0x1b, 0x6e, 0x5a, 0xa0, 0x09, 0x83, 0x2c, 0x1a,
        0x4a, 0x4c, 0x58, 0xcf, 0x6a, 0xcb, 0xbe, 0x39, 0x20, 0xfc, 0xb1, 0x5b, 0x53, 0xd1, 0x00, 0xed,
        0x71, 0xd8, 0x31, 0x15, 0x34, 0xa5, 0xe5, 0xf1, 0x36, 0x3f, 0xf7, 0xcc, 0xb7, 0xfd, 0x93, 0x26,
        0xeb, 0x27, 0xb2, 0x75, 0x07, 0x12, 0x80, 0xe2, 0x18, 0x96, 0x05, 0x9a, 0x04, 0xc7, 0x23, 0xc3,
        0xfe, 0xd7, 0xab, 0x76, 0x30, 0x01, 0x67, 0x2b, 0xf2, 0x6b, 0x6f, 0xc5, 0x63, 0x7c, 0x77, 0x7b,
        0x9c, 0xa4, 0x72, 0xc0, 0xad, 0xd4, 0xa2, 0xaf, 0xfa, 0x59, 0x47, 0xf0, 0xca, 0x82, 0xc9, 0x7d,
        0xce, 0x55, 0x28, 0xdf, 0x9b, 0x1e, 0x87, 0xe9, 0x69, 0xd9, 0x8e, 0x94, 0xe1, 0xf8, 0x98, 0x11,
        0xb0, 0x54, 0xbb, 0x16, 0x41, 0x99, 0x2d, 0x0f, 0xbf, 0xe6, 0x42, 0x68, 0x8c, 0xa1, 0x89, 0x0d,
        0x4b, 0xbd, 0x8b, 0x8a, 0xe8, 0xdd, 0x74, 0x1f, 0x1c, 0xa6, 0xb4, 0xc6, 0xba, 0x78, 0x25, 0x2e,
        0x86, 0xc1, 0x1d, 0x9e, 0x61, 0x35, 0x57, 0xb9, 0x48, 0x03, 0xf6, 0x0e, 0x70, 0x3e, 0xb5, 0x66,
        0x91, 0x95, 0xe4, 0x79, 0xc2, 0xd3, 0xac, 0x62, 0x49, 0x06, 0x24, 0x5c, 0xe0, 0x32, 0x3a, 0x0a,
        0x65, 0x7a, 0xae, 0x08, 0x6c, 0x56, 0xf4, 0xea, 0x8d, 0xd5, 0x4e, 0xa9, 0xe7, 0xc8, 0x37, 0x6d,
        0x64, 0x5d, 0x19, 0x73, 0xc4, 0xa7, 0x7e, 0x3d, 0x5f, 0x97, 0x44, 0x17, 0xcd, 0x0c, 0x13, 0xec,
        0xde, 0x5e, 0x0b, 0xdb, 0x46, 0xee, 0xb8, 0x14, 0x22, 0x2a, 0x90, 0x88, 0x60, 0x81, 0x4f, 0xdc
    },
    /*Round0 ḱ[1] is 0x61*/
    {
        0xef, 0xd0, 0xfb, 0xaa, 0x4d, 0x43, 0x85, 0x33, 0xf9, 0x45, 0x7f, 0x02, 0x3c, 0x50, 0xa8, 0x9f,
        0xa3, 0x51, 0x8f, 0x40, 0x9d, 0x92, 0xf5, 0x38, 0xb6, 0xbc, 0x21, 0xda, 0xff, 0x10, 0xd2, 0xf3,
        0x83, 0x09, 0x1a, 0x2c, 0x6e, 0x1b, 0xa0, 0x5a, 0x3b, 0x52, 0xb3, 0xd6, 0xe3, 0x29, 0x84, 0x2f,
        0xd1, 0x53, 0xed, 0x00, 0xfc, 0x20, 0x5b, 0xb1, 0xcb, 0x6a, 0x39, 0xbe, 0x4c, 0x4a, 0xcf, 0x58,
        0xfd, 0xb7, 0x26, 0x93, 0x3f, 0x36, 0xcc, 0xf7, 0xa5, 0x34, 0xf1, 0xe5, 0xd8, 0x71, 0x15, 0x31,
        0xc7, 0x04, 0xc3, 0x23, 0x96, 0x18, 0x9a, 0x05, 0x12, 0x07, 0xe2, 0x80, 0x27, 0xeb, 0x75, 0xb2,
        0x7c, 0x63, 0x7b, 0x77, 0x6b, 0xf2, 0xc5, 0x6f, 0x01, 0x30, 0x2b, 0x67, 0xd7, 0xfe, 0x76, 0xab,
        0x82, 0xca, 0x7d, 0xc9, 0x59, 0xfa, 0xf0, 0x47, 0xd4, 0xad, 0xaf, 0xa2, 0xa4, 0x9c, 0xc0, 0x72,
        0xf8, 0xe1, 0x11, 0x98, 0xd9, 0x69, 0x94, 0x8e, 0x1e, 0x9b, 0xe9, 0x87, 0x55, 0xce, 0xdf, 0x28,
        0xa1, 0x8c, 0x0d, 0x89, 0xe6, 0xbf, 0x68, 0x42, 0x99, 0x41, 0x0f, 0x2d, 0x54, 0xb0, 0x16, 0xbb,
        0x78, 0xba, 0x2e, 0x25, 0xa6, 0x1c, 0xc6, 0xb4, 0xdd, 0xe8, 0x1f, 0x74, 0xbd, 0x4b, 0x8a, 0x8b,
        0x3e, 0x70, 0x66, 0xb5, 0x03, 0x48, 0x0e, 0xf6, 0x35, 0x61, 0xb9, 0x57, 0xc1, 0x86, 0x9e, 0x1d,
        0x32, 0xe0, 0x0a, 0x3a, 0x06, 0x49, 0x5c, 0x24, 0xd3, 0xc2, 0x62, 0xac, 0x95, 0x91, 0x79, 0xe4,
        0xc8, 0xe7, 0x6d, 0x37, 0xd5, 0x8d, 0xa9, 0x4e, 0x56, 0x6c, 0xea, 0xf4, 0x7a, 0x65, 0x08, 0xae,
        0x0c, 0xcd, 0xec, 0x13, 0x97, 0x5f, 0x17, 0x44, 0xa7, 0xc4, 0x3d, 0x7e, 0x5d, 0x64, 0x73, 0x19,
        0x81, 0x60, 0xdc, 0x4f, 0x2a, 0x22, 0x88, 0x90, 0xee, 0x46, 0x14, 0xb8, 0x5e, 0xde, 0xdb, 0x0b
    },
...

T-boxesを用いた暗号化は下記の通りです。

各RoundのMixColumnsまた、4つのpre-computed LUT(M0, M1, M2, M3)で生成可能であり、T-boxesと結合されことができます。
参考にMixColumnsの場合、Rijndael's Galois Fieldの積であり、一般的な積がありません。


T-boxes+M-boxes(M_T-Boxes)は以下のように生成されことができます。
unsigned int M_T-boxesRound1[16][256] =
{   
    /*Round0 ḱ[0] is 0x6c*/
    {
        0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0xcf45458a, 0x10f9f9e9, 0x06020204, 0x817f7ffe, 0xc5434386, 0xd74d4d9a, 0x55333366, 0x94858511, 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed,
        0x30101020, 0x1affffe5, 0x0ef3f3fd, 0x6dd2d2bf, 0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x04f5f5f1, 0xf35151a2, 0xfea3a35d, 0xc0404080, 0x8a8f8f05,
        0x7b292952, 0x3ee3e3dd, 0x712f2f5e, 0x97848413, 0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b, 0x1b090912, 0x9e83831d, 0x742c2c58, 0x2e1a1a34,
        0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, 0xbe6a6ad4, 0x46cbcb8d, 0xd9bebe67, 0x4b393972, 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6, 0xf55353a6, 0x68d1d1b9, 0x00000000, 0x2cededc1,
        0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, 0x5c343468, 0xf4a5a551, 0x34e5e5d1, 0x08f1f1f9, 0x5a36366c, 0x413f3f7e, 0x02f7f7f5, 0x4fcccc83, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c,
        0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x0907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, 0x28181830, 0xa1969637, 0x0f05050a, 0xb59a9a2f, 0x0c040408, 0x52c7c795, 0x65232346, 0x5ec3c39d,
        0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0x50303060, 0x03010102, 0xa96767ce, 0x7d2b2b56, 0x0df2f2ff, 0xbd6b6bd6, 0xb16f6fde, 0x54c5c591, 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6,
        0xbf9c9c23, 0xf7a4a453, 0x967272e4, 0x5bc0c09b, 0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0x0bf0f0fb, 0x45caca8f, 0x9d82821f, 0x40c9c989, 0x877d7dfa,
        0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, 0xb69b9b2d, 0x221e1e3c, 0x92878715, 0x20e9e9c9, 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122,
        0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c, 0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, 0xdabfbf65, 0x31e6e6d7, 0xc6424284, 0xb86868d0, 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a,
        0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, 0x241c1c38, 0xf1a6a657, 0xc7b4b473, 0x51c6c697, 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c,
        0x91868617, 0x58c1c199, 0x271d1d3a, 0xb99e9e27, 0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0xd8484890, 0x05030306, 0x01f6f6f7, 0x120e0e1c, 0x907070e0, 0x423e3e7c, 0xc4b5b571, 0xaa6666cc,
        0xa8919139, 0xa4959531, 0x37e4e4d3, 0x8b7979f2, 0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xdb494992, 0x0a06060c, 0x6c242448, 0xe45c5cb8, 0x3be0e0db, 0x56323264, 0x4e3a3a74, 0x1e0a0a14,
        0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, 0xb46c6cd8, 0xfa5656ac, 0x07f4f4f3, 0x25eaeacf, 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda,
        0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, 0x57c4c493, 0xf2a7a755, 0x827e7efc, 0x473d3d7a, 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3,
        0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, 0x66222244, 0x7e2a2a54, 0xab90903b, 0x8388880b, 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3
    },
    ...

Encryption Function, TfcqPqf1lNhu0DC2qGsAAeML0SEmOBYX4jpYUnyT8qYWIlEq(unsigned__int8*in、unsigned__int8*out)を分析すると、以下のような流れで実行されます。

1. ShiftRows, lrsFdMdlAT0vSMVedxmqOkCBF7sCTbhCjYEp1rLP8vatWEGD( )

2. M_T-boxes based on encryption process(SubByte, AddRoundKey, MixColumns)

  • M_T-boxesを使用してデータ暗号化


     バイナリ内のM_T-Boxesは下記の通りです。





4. ShiftRows before last round

5. T-boxes based on last round encryption process(SubByte, AddRoundKey)

    バイナリ内のRound10のT-boxは下記の通りです。

Encrypted Flag、"g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc="を復号するためには、まずsecretKeyをrecoveryしなければなりません。

M-boxesはMixColumnsのPre-computed LUTとして ḱ1...16とは独立かつ任意に生成することができます。 M_T-boxesのRound1のLUTはḱ1...16に依存的なので、M-T-boxesからT-boxesを分離するなら、secetKeyも復元することができます。

下修飾で見られるように、xが0の場合(M_T-boxes[1...16][0])ḱ1...16 自体がindexになってしまいます。


したがって、以下のステップでsecretKeyを得ることができます。
  1. Round1のM_T-boxesを探す。
  2. M-boxesを生成する。
  3. Sbox(0...255)生成してindexで使用する。
    S(ḱ0[0...15])がM-boxesのindexがなるから
  4. M-boxes[index]値をもたらす。
  5. Round1のM_T-box[j][0]をもたらす。 j=1...15(ḱ0[1...15])
  6. Step 4のM-boxes[index]とM_T-boxes[j][0]を比較する。 もし両値が同じであればindexがḱ0[j]になる。
  7. 0はroundKey0(secretKey)をShiftRowsした結果なので、unShiftRowsをしてsecretKeyを得ることができる。

exploit codeは下記の通りです。
#!/usr/bin/python
# -*- coding: utf-8 -*-

import base64
from Crypto.Cipher import AES
import binascii

encFlag = "g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc="
print "encryptedFlag:"+ encFlag

Sbox = [
    0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76,
    0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0,
    0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15,
    0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75,
    0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84,
    0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF,
    0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8,
    0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2,
    0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73,
    0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB,
    0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79,
    0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08,
    0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A,
    0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E,
    0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF,
    0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16,
]

matrix_4x4 = [
 1, 2, 0, 0,
 0, 1, 2, 0,
 0, 0, 1, 2,
 2, 0, 0, 1
]

gmul = [
 [ 
  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F, 
  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1A, 0x1B, 0x1C, 0x1D, 0x1E, 0x1F, 
  0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2A, 0x2B, 0x2C, 0x2D, 0x2E, 0x2F, 
  0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3A, 0x3B, 0x3C, 0x3D, 0x3E, 0x3F, 
  0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4A, 0x4B, 0x4C, 0x4D, 0x4E, 0x4F, 
  0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5A, 0x5B, 0x5C, 0x5D, 0x5E, 0x5F, 
  0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6A, 0x6B, 0x6C, 0x6D, 0x6E, 0x6F, 
  0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7A, 0x7B, 0x7C, 0x7D, 0x7E, 0x7F, 
  0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8A, 0x8B, 0x8C, 0x8D, 0x8E, 0x8F, 
  0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9A, 0x9B, 0x9C, 0x9D, 0x9E, 0x9F, 
  0xA0, 0xA1, 0xA2, 0xA3, 0xA4, 0xA5, 0xA6, 0xA7, 0xA8, 0xA9, 0xAA, 0xAB, 0xAC, 0xAD, 0xAE, 0xAF, 
  0xB0, 0xB1, 0xB2, 0xB3, 0xB4, 0xB5, 0xB6, 0xB7, 0xB8, 0xB9, 0xBA, 0xBB, 0xBC, 0xBD, 0xBE, 0xBF, 
  0xC0, 0xC1, 0xC2, 0xC3, 0xC4, 0xC5, 0xC6, 0xC7, 0xC8, 0xC9, 0xCA, 0xCB, 0xCC, 0xCD, 0xCE, 0xCF, 
  0xD0, 0xD1, 0xD2, 0xD3, 0xD4, 0xD5, 0xD6, 0xD7, 0xD8, 0xD9, 0xDA, 0xDB, 0xDC, 0xDD, 0xDE, 0xDF, 
  0xE0, 0xE1, 0xE2, 0xE3, 0xE4, 0xE5, 0xE6, 0xE7, 0xE8, 0xE9, 0xEA, 0xEB, 0xEC, 0xED, 0xEE, 0xEF, 
  0xF0, 0xF1, 0xF2, 0xF3, 0xF4, 0xF5, 0xF6, 0xF7, 0xF8, 0xF9, 0xFA, 0xFB, 0xFC, 0xFD, 0xFE, 0xFF 
 ],
 [ 
  0x00, 0x02, 0x04, 0x06, 0x08, 0x0A, 0x0C, 0x0E, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1A, 0x1C, 0x1E, 
  0x20, 0x22, 0x24, 0x26, 0x28, 0x2A, 0x2C, 0x2E, 0x30, 0x32, 0x34, 0x36, 0x38, 0x3A, 0x3C, 0x3E, 
  0x40, 0x42, 0x44, 0x46, 0x48, 0x4A, 0x4C, 0x4E, 0x50, 0x52, 0x54, 0x56, 0x58, 0x5A, 0x5C, 0x5E, 
  0x60, 0x62, 0x64, 0x66, 0x68, 0x6A, 0x6C, 0x6E, 0x70, 0x72, 0x74, 0x76, 0x78, 0x7A, 0x7C, 0x7E, 
  0x80, 0x82, 0x84, 0x86, 0x88, 0x8A, 0x8C, 0x8E, 0x90, 0x92, 0x94, 0x96, 0x98, 0x9A, 0x9C, 0x9E, 
  0xA0, 0xA2, 0xA4, 0xA6, 0xA8, 0xAA, 0xAC, 0xAE, 0xB0, 0xB2, 0xB4, 0xB6, 0xB8, 0xBA, 0xBC, 0xBE, 
  0xC0, 0xC2, 0xC4, 0xC6, 0xC8, 0xCA, 0xCC, 0xCE, 0xD0, 0xD2, 0xD4, 0xD6, 0xD8, 0xDA, 0xDC, 0xDE, 
  0xE0, 0xE2, 0xE4, 0xE6, 0xE8, 0xEA, 0xEC, 0xEE, 0xF0, 0xF2, 0xF4, 0xF6, 0xF8, 0xFA, 0xFC, 0xFE, 
  0x1B, 0x19, 0x1F, 0x1D, 0x13, 0x11, 0x17, 0x15, 0x0B, 0x09, 0x0F, 0x0D, 0x03, 0x01, 0x07, 0x05, 
  0x3B, 0x39, 0x3F, 0x3D, 0x33, 0x31, 0x37, 0x35, 0x2B, 0x29, 0x2F, 0x2D, 0x23, 0x21, 0x27, 0x25, 
  0x5B, 0x59, 0x5F, 0x5D, 0x53, 0x51, 0x57, 0x55, 0x4B, 0x49, 0x4F, 0x4D, 0x43, 0x41, 0x47, 0x45, 
  0x7B, 0x79, 0x7F, 0x7D, 0x73, 0x71, 0x77, 0x75, 0x6B, 0x69, 0x6F, 0x6D, 0x63, 0x61, 0x67, 0x65, 
  0x9B, 0x99, 0x9F, 0x9D, 0x93, 0x91, 0x97, 0x95, 0x8B, 0x89, 0x8F, 0x8D, 0x83, 0x81, 0x87, 0x85, 
  0xBB, 0xB9, 0xBF, 0xBD, 0xB3, 0xB1, 0xB7, 0xB5, 0xAB, 0xA9, 0xAF, 0xAD, 0xA3, 0xA1, 0xA7, 0xA5, 
  0xDB, 0xD9, 0xDF, 0xDD, 0xD3, 0xD1, 0xD7, 0xD5, 0xCB, 0xC9, 0xCF, 0xCD, 0xC3, 0xC1, 0xC7, 0xC5,
  0xFB, 0xF9, 0xFF, 0xFD, 0xF3, 0xF1, 0xF7, 0xF5, 0xEB, 0xE9, 0xEF, 0xED, 0xE3, 0xE1, 0xE7, 0xE5 
 ],
 [ 
  0x00, 0x03, 0x06, 0x05, 0x0C, 0x0F, 0x0A, 0x09, 0x18, 0x1B, 0x1E, 0x1D, 0x14, 0x17, 0x12, 0x11, 
  0x30, 0x33, 0x36, 0x35, 0x3C, 0x3F, 0x3A, 0x39, 0x28, 0x2B, 0x2E, 0x2D, 0x24, 0x27, 0x22, 0x21, 
  0x60, 0x63, 0x66, 0x65, 0x6C, 0x6F, 0x6A, 0x69, 0x78, 0x7B, 0x7E, 0x7D, 0x74, 0x77, 0x72, 0x71, 
  0x50, 0x53, 0x56, 0x55, 0x5C, 0x5F, 0x5A, 0x59, 0x48, 0x4B, 0x4E, 0x4D, 0x44, 0x47, 0x42, 0x41, 
  0xC0, 0xC3, 0xC6, 0xC5, 0xCC, 0xCF, 0xCA, 0xC9, 0xD8, 0xDB, 0xDE, 0xDD, 0xD4, 0xD7, 0xD2, 0xD1, 
  0xF0, 0xF3, 0xF6, 0xF5, 0xFC, 0xFF, 0xFA, 0xF9, 0xE8, 0xEB, 0xEE, 0xED, 0xE4, 0xE7, 0xE2, 0xE1, 
  0xA0, 0xA3, 0xA6, 0xA5, 0xAC, 0xAF, 0xAA, 0xA9, 0xB8, 0xBB, 0xBE, 0xBD, 0xB4, 0xB7, 0xB2, 0xB1, 
  0x90, 0x93, 0x96, 0x95, 0x9C, 0x9F, 0x9A, 0x99, 0x88, 0x8B, 0x8E, 0x8D, 0x84, 0x87, 0x82, 0x81, 
  0x9B, 0x98, 0x9D, 0x9E, 0x97, 0x94, 0x91, 0x92, 0x83, 0x80, 0x85, 0x86, 0x8F, 0x8C, 0x89, 0x8A, 
  0xAB, 0xA8, 0xAD, 0xAE, 0xA7, 0xA4, 0xA1, 0xA2, 0xB3, 0xB0, 0xB5, 0xB6, 0xBF, 0xBC, 0xB9, 0xBA, 
  0xFB, 0xF8, 0xFD, 0xFE, 0xF7, 0xF4, 0xF1, 0xF2, 0xE3, 0xE0, 0xE5, 0xE6, 0xEF, 0xEC, 0xE9, 0xEA, 
  0xCB, 0xC8, 0xCD, 0xCE, 0xC7, 0xC4, 0xC1, 0xC2, 0xD3, 0xD0, 0xD5, 0xD6, 0xDF, 0xDC, 0xD9, 0xDA, 
  0x5B, 0x58, 0x5D, 0x5E, 0x57, 0x54, 0x51, 0x52, 0x43, 0x40, 0x45, 0x46, 0x4F, 0x4C, 0x49, 0x4A, 
  0x6B, 0x68, 0x6D, 0x6E, 0x67, 0x64, 0x61, 0x62, 0x73, 0x70, 0x75, 0x76, 0x7F, 0x7C, 0x79, 0x7A, 
  0x3B, 0x38, 0x3D, 0x3E, 0x37, 0x34, 0x31, 0x32, 0x23, 0x20, 0x25, 0x26, 0x2F, 0x2C, 0x29, 0x2A, 
  0x0B, 0x08, 0x0D, 0x0E, 0x07, 0x04, 0x01, 0x02, 0x13, 0x10, 0x15, 0x16, 0x1F, 0x1C, 0x19, 0x1A 
 ]
];

M_TBoxesR0 = [
 [
     0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0xcf45458a, 0x10f9f9e9, 0x06020204, 0x817f7ffe, 0xc5434386, 0xd74d4d9a, 0x55333366, 0x94858511, 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed,
     0x30101020, 0x1affffe5, 0x0ef3f3fd, 0x6dd2d2bf, 0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x04f5f5f1, 0xf35151a2, 0xfea3a35d, 0xc0404080, 0x8a8f8f05,
     0x7b292952, 0x3ee3e3dd, 0x712f2f5e, 0x97848413, 0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b, 0x1b090912, 0x9e83831d, 0x742c2c58, 0x2e1a1a34,
     0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, 0xbe6a6ad4, 0x46cbcb8d, 0xd9bebe67, 0x4b393972, 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6, 0xf55353a6, 0x68d1d1b9, 0x00000000, 0x2cededc1,
     0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, 0x5c343468, 0xf4a5a551, 0x34e5e5d1, 0x08f1f1f9, 0x5a36366c, 0x413f3f7e, 0x02f7f7f5, 0x4fcccc83, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c,
     0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x0907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, 0x28181830, 0xa1969637, 0x0f05050a, 0xb59a9a2f, 0x0c040408, 0x52c7c795, 0x65232346, 0x5ec3c39d,
     0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0x50303060, 0x03010102, 0xa96767ce, 0x7d2b2b56, 0x0df2f2ff, 0xbd6b6bd6, 0xb16f6fde, 0x54c5c591, 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6,
     0xbf9c9c23, 0xf7a4a453, 0x967272e4, 0x5bc0c09b, 0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0x0bf0f0fb, 0x45caca8f, 0x9d82821f, 0x40c9c989, 0x877d7dfa,
     0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, 0xb69b9b2d, 0x221e1e3c, 0x92878715, 0x20e9e9c9, 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122,
     0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c, 0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, 0xdabfbf65, 0x31e6e6d7, 0xc6424284, 0xb86868d0, 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a,
     0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, 0x241c1c38, 0xf1a6a657, 0xc7b4b473, 0x51c6c697, 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c,
     0x91868617, 0x58c1c199, 0x271d1d3a, 0xb99e9e27, 0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0xd8484890, 0x05030306, 0x01f6f6f7, 0x120e0e1c, 0x907070e0, 0x423e3e7c, 0xc4b5b571, 0xaa6666cc,
     0xa8919139, 0xa4959531, 0x37e4e4d3, 0x8b7979f2, 0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xdb494992, 0x0a06060c, 0x6c242448, 0xe45c5cb8, 0x3be0e0db, 0x56323264, 0x4e3a3a74, 0x1e0a0a14,
     0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, 0xb46c6cd8, 0xfa5656ac, 0x07f4f4f3, 0x25eaeacf, 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda,
     0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, 0x57c4c493, 0xf2a7a755, 0x827e7efc, 0x473d3d7a, 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3,
     0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, 0x66222244, 0x7e2a2a54, 0xab90903b, 0x8388880b, 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3
 ],
 [
     0xefefc52a, 0xd0d0bb6b, 0xfbfbed16, 0xaaaa4fe5, 0x4d4d9ad7, 0x434386c5, 0x85851194, 0x33336655, 0xf9f9e910, 0x45458acf, 0x7f7ffe81, 0x02020406, 0x3c3c7844, 0x5050a0f0, 0xa8a84be3, 0x9f9f25ba,
     0xa3a35dfe, 0x5151a2f3, 0x8f8f058a, 0x404080c0, 0x9d9d21bc, 0x92923fad, 0xf5f5f104, 0x38387048, 0xb6b677c1, 0xbcbc63df, 0x21214263, 0xdadaaf75, 0xffffe51a, 0x10102030, 0xd2d2bf6d, 0xf3f3fd0e,
     0x83831d9e, 0x0909121b, 0x1a1a342e, 0x2c2c5874, 0x6e6edcb2, 0x1b1b362d, 0xa0a05bfb, 0x5a5ab4ee, 0x3b3b764d, 0x5252a4f6, 0xb3b37dce, 0xd6d6b761, 0xe3e3dd3e, 0x2929527b, 0x84841397, 0x2f2f5e71,
     0xd1d1b968, 0x5353a6f5, 0xededc12c, 0x00000000, 0xfcfce31f, 0x20204060, 0x5b5bb6ed, 0xb1b179c8, 0xcbcb8d46, 0x6a6ad4be, 0x3939724b, 0xbebe67d9, 0x4c4c98d4, 0x4a4a94de, 0xcfcf854a, 0x5858b0e8,
     0xfdfde11c, 0xb7b775c2, 0x26264c6a, 0x93933dae, 0x3f3f7e41, 0x36366c5a, 0xcccc834f, 0xf7f7f502, 0xa5a551f4, 0x3434685c, 0xf1f1f908, 0xe5e5d134, 0xd8d8ab73, 0x7171e293, 0x15152a3f, 0x31316253,
     0xc7c79552, 0x0404080c, 0xc3c39d5e, 0x23234665, 0x969637a1, 0x18183028, 0x9a9a2fb5, 0x05050a0f, 0x12122436, 0x07070e09, 0xe2e2df3d, 0x80801b9b, 0x27274e69, 0xebebcd26, 0x7575ea9f, 0xb2b27fcd,
     0x7c7cf884, 0x6363c6a5, 0x7b7bf68d, 0x7777ee99, 0x6b6bd6bd, 0xf2f2ff0d, 0xc5c59154, 0x6f6fdeb1, 0x01010203, 0x30306050, 0x2b2b567d, 0x6767cea9, 0xd7d7b562, 0xfefee719, 0x7676ec9a, 0xabab4de6,
     0x82821f9d, 0xcaca8f45, 0x7d7dfa87, 0xc9c98940, 0x5959b2eb, 0xfafaef15, 0xf0f0fb0b, 0x47478ec9, 0xd4d4b367, 0xadad41ec, 0xafaf45ea, 0xa2a25ffd, 0xa4a453f7, 0x9c9c23bf, 0xc0c09b5b, 0x7272e496,
     0xf8f8eb13, 0xe1e1d938, 0x11112233, 0x98982bb3, 0xd9d9a970, 0x6969d2bb, 0x949433a7, 0x8e8e0789, 0x1e1e3c22, 0x9b9b2db6, 0xe9e9c920, 0x87871592, 0x5555aaff, 0xcece8749, 0xdfdfa57a, 0x28285078,
     0xa1a159f8, 0x8c8c038f, 0x0d0d1a17, 0x89890980, 0xe6e6d731, 0xbfbf65da, 0x6868d0b8, 0x424284c6, 0x999929b0, 0x414182c3, 0x0f0f1e11, 0x2d2d5a77, 0x5454a8fc, 0xb0b07bcb, 0x16162c3a, 0xbbbb6dd6,
     0x7878f088, 0xbaba6fd5, 0x2e2e5c72, 0x25254a6f, 0xa6a657f1, 0x1c1c3824, 0xc6c69751, 0xb4b473c7, 0xdddda17c, 0xe8e8cb23, 0x1f1f3e21, 0x7474e89c, 0xbdbd61dc, 0x4b4b96dd, 0x8a8a0f85, 0x8b8b0d86,
     0x3e3e7c42, 0x7070e090, 0x6666ccaa, 0xb5b571c4, 0x03030605, 0x484890d8, 0x0e0e1c12, 0xf6f6f701, 0x35356a5f, 0x6161c2a3, 0xb9b969d0, 0x5757aef9, 0xc1c19958, 0x86861791, 0x9e9e27b9, 0x1d1d3a27,
     0x32326456, 0xe0e0db3b, 0x0a0a141e, 0x3a3a744e, 0x06060c0a, 0x494992db, 0x5c5cb8e4, 0x2424486c, 0xd3d3bd6e, 0xc2c29f5d, 0x6262c4a6, 0xacac43ef, 0x959531a4, 0x919139a8, 0x7979f28b, 0xe4e4d337,
     0xc8c88b43, 0xe7e7d532, 0x6d6ddab7, 0x37376e59, 0xd5d5b164, 0x8d8d018c, 0xa9a949e0, 0x4e4e9cd2, 0x5656acfa, 0x6c6cd8b4, 0xeaeacf25, 0xf4f4f307, 0x7a7af48e, 0x6565caaf, 0x08081018, 0xaeae47e9,
     0x0c0c1814, 0xcdcd814c, 0xececc32f, 0x13132635, 0x979735a2, 0x5f5fbee1, 0x17172e39, 0x444488cc, 0xa7a755f2, 0xc4c49357, 0x3d3d7a47, 0x7e7efc82, 0x5d5dbae7, 0x6464c8ac, 0x7373e695, 0x1919322b,
     0x81811998, 0x6060c0a0, 0xdcdca37f, 0x4f4f9ed1, 0x2a2a547e, 0x22224466, 0x88880b83, 0x90903bab, 0xeeeec729, 0x46468cca, 0x1414283c, 0xb8b86bd3, 0x5e5ebce2, 0xdedea779, 0xdbdbad76, 0x0b0b161d
 ],
 [
     0x070e0907, 0x12243612, 0x801b9b80, 0xe2df3de2, 0xebcd26eb, 0x274e6927, 0xb27fcdb2, 0x75ea9f75, 0x04080c04, 0xc79552c7, 0x23466523, 0xc39d5ec3, 0x18302818, 0x9637a196, 0x050a0f05, 0x9a2fb59a,
     0x34685c34, 0xa551f4a5, 0xe5d134e5, 0xf1f908f1, 0x71e29371, 0xd8ab73d8, 0x31625331, 0x152a3f15, 0xb775c2b7, 0xfde11cfd, 0x933dae93, 0x264c6a26, 0x366c5a36, 0x3f7e413f, 0xf7f502f7, 0xcc834fcc,
     0xad41ecad, 0xd4b367d4, 0xa25ffda2, 0xaf45eaaf, 0x9c23bf9c, 0xa453f7a4, 0x72e49672, 0xc09b5bc0, 0xca8f45ca, 0x821f9d82, 0xc98940c9, 0x7dfa877d, 0xfaef15fa, 0x59b2eb59, 0x478ec947, 0xf0fb0bf0,
     0x30605030, 0x01020301, 0x67cea967, 0x2b567d2b, 0xfee719fe, 0xd7b562d7, 0xab4de6ab, 0x76ec9a76, 0x63c6a563, 0x7cf8847c, 0x77ee9977, 0x7bf68d7b, 0xf2ff0df2, 0x6bd6bd6b, 0x6fdeb16f, 0xc59154c5,
     0xbc63dfbc, 0xb677c1b6, 0xdaaf75da, 0x21426321, 0x10203010, 0xffe51aff, 0xf3fd0ef3, 0xd2bf6dd2, 0x51a2f351, 0xa35dfea3, 0x4080c040, 0x8f058a8f, 0x923fad92, 0x9d21bc9d, 0x38704838, 0xf5f104f5,
     0x458acf45, 0xf9e910f9, 0x02040602, 0x7ffe817f, 0x50a0f050, 0x3c78443c, 0x9f25ba9f, 0xa84be3a8, 0xd0bb6bd0, 0xefc52aef, 0xaa4fe5aa, 0xfbed16fb, 0x4386c543, 0x4d9ad74d, 0x33665533, 0x85119485,
     0x6ad4be6a, 0xcb8d46cb, 0xbe67d9be, 0x39724b39, 0x4a94de4a, 0x4c98d44c, 0x58b0e858, 0xcf854acf, 0x53a6f553, 0xd1b968d1, 0x00000000, 0xedc12ced, 0x20406020, 0xfce31ffc, 0xb179c8b1, 0x5bb6ed5b,
     0x52a4f652, 0x3b764d3b, 0xd6b761d6, 0xb37dceb3, 0x29527b29, 0xe3dd3ee3, 0x2f5e712f, 0x84139784, 0x09121b09, 0x831d9e83, 0x2c58742c, 0x1a342e1a, 0x1b362d1b, 0x6edcb26e, 0x5ab4ee5a, 0xa05bfba0,
     0x6cd8b46c, 0x56acfa56, 0xf4f307f4, 0xeacf25ea, 0x65caaf65, 0x7af48e7a, 0xae47e9ae, 0x08101808, 0xe7d532e7, 0xc88b43c8, 0x376e5937, 0x6ddab76d, 0x8d018c8d, 0xd5b164d5, 0x4e9cd24e, 0xa949e0a9,
     0xc29f5dc2, 0xd3bd6ed3, 0xac43efac, 0x62c4a662, 0x9139a891, 0x9531a495, 0xe4d337e4, 0x79f28b79, 0xe0db3be0, 0x32645632, 0x3a744e3a, 0x0a141e0a, 0x4992db49, 0x060c0a06, 0x24486c24, 0x5cb8e45c,
     0x468cca46, 0xeec729ee, 0xb86bd3b8, 0x14283c14, 0xdea779de, 0x5ebce25e, 0x0b161d0b, 0xdbad76db, 0x60c0a060, 0x81199881, 0x4f9ed14f, 0xdca37fdc, 0x22446622, 0x2a547e2a, 0x903bab90, 0x880b8388,
     0xc49357c4, 0xa755f2a7, 0x7efc827e, 0x3d7a473d, 0x64c8ac64, 0x5dbae75d, 0x19322b19, 0x73e69573, 0xcd814ccd, 0x0c18140c, 0x13263513, 0xecc32fec, 0x5fbee15f, 0x9735a297, 0x4488cc44, 0x172e3917,
     0x4182c341, 0x9929b099, 0x2d5a772d, 0x0f1e110f, 0xb07bcbb0, 0x54a8fc54, 0xbb6dd6bb, 0x162c3a16, 0x8c038f8c, 0xa159f8a1, 0x89098089, 0x0d1a170d, 0xbf65dabf, 0xe6d731e6, 0x4284c642, 0x68d0b868,
     0x9b2db69b, 0x1e3c221e, 0x87159287, 0xe9c920e9, 0xce8749ce, 0x55aaff55, 0x28507828, 0xdfa57adf, 0xe1d938e1, 0xf8eb13f8, 0x982bb398, 0x11223311, 0x69d2bb69, 0xd9a970d9, 0x8e07898e, 0x9433a794,
     0x61c2a361, 0x356a5f35, 0x57aef957, 0xb969d0b9, 0x86179186, 0xc19958c1, 0x1d3a271d, 0x9e27b99e, 0x70e09070, 0x3e7c423e, 0xb571c4b5, 0x66ccaa66, 0x4890d848, 0x03060503, 0xf6f701f6, 0x0e1c120e,
     0xe8cb23e8, 0xdda17cdd, 0x74e89c74, 0x1f3e211f, 0x4b96dd4b, 0xbd61dcbd, 0x8b0d868b, 0x8a0f858a, 0xba6fd5ba, 0x78f08878, 0x254a6f25, 0x2e5c722e, 0x1c38241c, 0xa657f1a6, 0xb473c7b4, 0xc69751c6
 ],
 [
     0xdcb26e6e, 0x362d1b1b, 0x5bfba0a0, 0xb4ee5a5a, 0x1d9e8383, 0x121b0909, 0x342e1a1a, 0x58742c2c, 0xdd3ee3e3, 0x527b2929, 0x13978484, 0x5e712f2f, 0x764d3b3b, 0xa4f65252, 0x7dceb3b3, 0xb761d6d6,
     0xe31ffcfc, 0x40602020, 0xb6ed5b5b, 0x79c8b1b1, 0xb968d1d1, 0xa6f55353, 0xc12ceded, 0x00000000, 0x98d44c4c, 0x94de4a4a, 0x854acfcf, 0xb0e85858, 0x8d46cbcb, 0xd4be6a6a, 0x724b3939, 0x67d9bebe,
     0x9ad74d4d, 0x86c54343, 0x11948585, 0x66553333, 0xc52aefef, 0xbb6bd0d0, 0xed16fbfb, 0x4fe5aaaa, 0x78443c3c, 0xa0f05050, 0x4be3a8a8, 0x25ba9f9f, 0xe910f9f9, 0x8acf4545, 0xfe817f7f, 0x04060202,
     0x21bc9d9d, 0x3fad9292, 0xf104f5f5, 0x70483838, 0x5dfea3a3, 0xa2f35151, 0x058a8f8f, 0x80c04040, 0xe51affff, 0x20301010, 0xbf6dd2d2, 0xfd0ef3f3, 0x77c1b6b6, 0x63dfbcbc, 0x42632121, 0xaf75dada,
     0xd6bd6b6b, 0xff0df2f2, 0x9154c5c5, 0xdeb16f6f, 0xf8847c7c, 0xc6a56363, 0xf68d7b7b, 0xee997777, 0xb562d7d7, 0xe719fefe, 0xec9a7676, 0x4de6abab, 0x02030101, 0x60503030, 0x567d2b2b, 0xcea96767,
     0xb2eb5959, 0xef15fafa, 0xfb0bf0f0, 0x8ec94747, 0x1f9d8282, 0x8f45caca, 0xfa877d7d, 0x8940c9c9, 0x53f7a4a4, 0x23bf9c9c, 0x9b5bc0c0, 0xe4967272, 0xb367d4d4, 0x41ecadad, 0x45eaafaf, 0x5ffda2a2,
     0x7e413f3f, 0x6c5a3636, 0x834fcccc, 0xf502f7f7, 0xe11cfdfd, 0x75c2b7b7, 0x4c6a2626, 0x3dae9393, 0xab73d8d8, 0xe2937171, 0x2a3f1515, 0x62533131, 0x51f4a5a5, 0x685c3434, 0xf908f1f1, 0xd134e5e5,
     0x37a19696, 0x30281818, 0x2fb59a9a, 0x0a0f0505, 0x9552c7c7, 0x080c0404, 0x9d5ec3c3, 0x46652323, 0x4e692727, 0xcd26ebeb, 0xea9f7575, 0x7fcdb2b2, 0x24361212, 0x0e090707, 0xdf3de2e2, 0x1b9b8080,
     0x57f1a6a6, 0x38241c1c, 0x9751c6c6, 0x73c7b4b4, 0xf0887878, 0x6fd5baba, 0x5c722e2e, 0x4a6f2525, 0x61dcbdbd, 0x96dd4b4b, 0x0f858a8a, 0x0d868b8b, 0xa17cdddd, 0xcb23e8e8, 0x3e211f1f, 0xe89c7474,
     0x06050303, 0x90d84848, 0x1c120e0e, 0xf701f6f6, 0x7c423e3e, 0xe0907070, 0xccaa6666, 0x71c4b5b5, 0x9958c1c1, 0x17918686, 0x27b99e9e, 0x3a271d1d, 0x6a5f3535, 0xc2a36161, 0x69d0b9b9, 0xaef95757,
     0xa970d9d9, 0xd2bb6969, 0x33a79494, 0x07898e8e, 0xeb13f8f8, 0xd938e1e1, 0x22331111, 0x2bb39898, 0xaaff5555, 0x8749cece, 0xa57adfdf, 0x50782828, 0x3c221e1e, 0x2db69b9b, 0xc920e9e9, 0x15928787,
     0xd731e6e6, 0x65dabfbf, 0xd0b86868, 0x84c64242, 0x59f8a1a1, 0x038f8c8c, 0x1a170d0d, 0x09808989, 0xa8fc5454, 0x7bcbb0b0, 0x2c3a1616, 0x6dd6bbbb, 0x29b09999, 0x82c34141, 0x1e110f0f, 0x5a772d2d,
     0x35a29797, 0xbee15f5f, 0x2e391717, 0x88cc4444, 0x18140c0c, 0x814ccdcd, 0xc32fecec, 0x26351313, 0xbae75d5d, 0xc8ac6464, 0xe6957373, 0x322b1919, 0x55f2a7a7, 0x9357c4c4, 0x7a473d3d, 0xfc827e7e,
     0x547e2a2a, 0x44662222, 0x0b838888, 0x3bab9090, 0x19988181, 0xc0a06060, 0xa37fdcdc, 0x9ed14f4f, 0xbce25e5e, 0xa779dede, 0xad76dbdb, 0x161d0b0b, 0xc729eeee, 0x8cca4646, 0x283c1414, 0x6bd3b8b8,
     0x0c0a0606, 0x92db4949, 0xb8e45c5c, 0x486c2424, 0x64563232, 0xdb3be0e0, 0x141e0a0a, 0x744e3a3a, 0x31a49595, 0x39a89191, 0xf28b7979, 0xd337e4e4, 0xbd6ed3d3, 0x9f5dc2c2, 0xc4a66262, 0x43efacac,
     0xb164d5d5, 0x018c8d8d, 0x49e0a9a9, 0x9cd24e4e, 0x8b43c8c8, 0xd532e7e7, 0xdab76d6d, 0x6e593737, 0xf48e7a7a, 0xcaaf6565, 0x10180808, 0x47e9aeae, 0xacfa5656, 0xd8b46c6c, 0xcf25eaea, 0xf307f4f4
 ],
 [
     0xeaafaf45, 0xfda2a25f, 0x67d4d4b3, 0xecadad41, 0x5bc0c09b, 0x967272e4, 0xf7a4a453, 0xbf9c9c23, 0x877d7dfa, 0x40c9c989, 0x9d82821f, 0x45caca8f, 0x0bf0f0fb, 0xc947478e, 0xeb5959b2, 0x15fafaef,
     0x7d2b2b56, 0xa96767ce, 0x03010102, 0x50303060, 0x9a7676ec, 0xe6abab4d, 0x62d7d7b5, 0x19fefee7, 0x8d7b7bf6, 0x997777ee, 0x847c7cf8, 0xa56363c6, 0x54c5c591, 0xb16f6fde, 0xbd6b6bd6, 0x0df2f2ff,
     0x3de2e2df, 0x9b80801b, 0x36121224, 0x0907070e, 0x9f7575ea, 0xcdb2b27f, 0x6927274e, 0x26ebebcd, 0x5ec3c39d, 0x65232346, 0x52c7c795, 0x0c040408, 0xb59a9a2f, 0x0f05050a, 0xa1969637, 0x28181830,
     0x08f1f1f9, 0x34e5e5d1, 0xf4a5a551, 0x5c343468, 0x3f15152a, 0x53313162, 0x73d8d8ab, 0x937171e2, 0x6a26264c, 0xae93933d, 0x1cfdfde1, 0xc2b7b775, 0x4fcccc83, 0x02f7f7f5, 0x413f3f7e, 0x5a36366c,
     0x4b393972, 0xd9bebe67, 0x46cbcb8d, 0xbe6a6ad4, 0x4acfcf85, 0xe85858b0, 0xd44c4c98, 0xde4a4a94, 0x2cededc1, 0x00000000, 0x68d1d1b9, 0xf55353a6, 0xed5b5bb6, 0xc8b1b179, 0x1ffcfce3, 0x60202040,
     0xceb3b37d, 0x61d6d6b7, 0x4d3b3b76, 0xf65252a4, 0x97848413, 0x712f2f5e, 0x3ee3e3dd, 0x7b292952, 0x2e1a1a34, 0x742c2c58, 0x9e83831d, 0x1b090912, 0xfba0a05b, 0xee5a5ab4, 0xb26e6edc, 0x2d1b1b36,
     0x63212142, 0x75dadaaf, 0xc1b6b677, 0xdfbcbc63, 0x6dd2d2bf, 0x0ef3f3fd, 0x1affffe5, 0x30101020, 0x8a8f8f05, 0xc0404080, 0xfea3a35d, 0xf35151a2, 0x04f5f5f1, 0x48383870, 0xbc9d9d21, 0xad92923f,
     0x817f7ffe, 0x06020204, 0x10f9f9e9, 0xcf45458a, 0xe3a8a84b, 0xba9f9f25, 0x443c3c78, 0xf05050a0, 0x16fbfbed, 0xe5aaaa4f, 0x2aefefc5, 0x6bd0d0bb, 0x94858511, 0x55333366, 0xd74d4d9a, 0xc5434386,
     0x3c141428, 0xd3b8b86b, 0x29eeeec7, 0xca46468c, 0x76dbdbad, 0x1d0b0b16, 0xe25e5ebc, 0x79dedea7, 0x7fdcdca3, 0xd14f4f9e, 0x98818119, 0xa06060c0, 0x8388880b, 0xab90903b, 0x7e2a2a54, 0x66222244,
     0x473d3d7a, 0x827e7efc, 0xf2a7a755, 0x57c4c493, 0x957373e6, 0x2b191932, 0xe75d5dba, 0xac6464c8, 0x2fececc3, 0x35131326, 0x140c0c18, 0x4ccdcd81, 0x3917172e, 0xcc444488, 0xa2979735, 0xe15f5fbe,
     0x25eaeacf, 0x07f4f4f3, 0xfa5656ac, 0xb46c6cd8, 0x18080810, 0xe9aeae47, 0x8e7a7af4, 0xaf6565ca, 0xb76d6dda, 0x5937376e, 0x43c8c88b, 0x32e7e7d5, 0xe0a9a949, 0xd24e4e9c, 0x64d5d5b1, 0x8c8d8d01,
     0xa66262c4, 0xefacac43, 0x6ed3d3bd, 0x5dc2c29f, 0x8b7979f2, 0x37e4e4d3, 0xa4959531, 0xa8919139, 0x1e0a0a14, 0x4e3a3a74, 0x56323264, 0x3be0e0db, 0xe45c5cb8, 0x6c242448, 0x0a06060c, 0xdb494992,
     0xd0b9b969, 0xf95757ae, 0x5f35356a, 0xa36161c2, 0xb99e9e27, 0x271d1d3a, 0x58c1c199, 0x91868617, 0xaa6666cc, 0xc4b5b571, 0x423e3e7c, 0x907070e0, 0x120e0e1c, 0x01f6f6f7, 0x05030306, 0xd8484890,
     0x211f1f3e, 0x9c7474e8, 0x7cdddda1, 0x23e8e8cb, 0x858a8a0f, 0x868b8b0d, 0xdcbdbd61, 0xdd4b4b96, 0x722e2e5c, 0x6f25254a, 0x887878f0, 0xd5baba6f, 0x51c6c697, 0xc7b4b473, 0xf1a6a657, 0x241c1c38,
     0x110f0f1e, 0x772d2d5a, 0xb0999929, 0xc3414182, 0x3a16162c, 0xd6bbbb6d, 0xfc5454a8, 0xcbb0b07b, 0x170d0d1a, 0x80898909, 0xf8a1a159, 0x8f8c8c03, 0xb86868d0, 0xc6424284, 0x31e6e6d7, 0xdabfbf65,
     0x20e9e9c9, 0x92878715, 0x221e1e3c, 0xb69b9b2d, 0x7adfdfa5, 0x78282850, 0xff5555aa, 0x49cece87, 0x33111122, 0xb398982b, 0x13f8f8eb, 0x38e1e1d9, 0xa7949433, 0x898e8e07, 0x70d9d9a9, 0xbb6969d2
 ],
 [
     0x404080c0, 0x8f8f058a, 0x5151a2f3, 0xa3a35dfe, 0x38387048, 0xf5f5f104, 0x92923fad, 0x9d9d21bc, 0xdadaaf75, 0x21214263, 0xbcbc63df, 0xb6b677c1, 0xf3f3fd0e, 0xd2d2bf6d, 0x10102030, 0xffffe51a,
     0xaaaa4fe5, 0xfbfbed16, 0xd0d0bb6b, 0xefefc52a, 0x33336655, 0x85851194, 0x434386c5, 0x4d4d9ad7, 0x02020406, 0x7f7ffe81, 0x45458acf, 0xf9f9e910, 0x9f9f25ba, 0xa8a84be3, 0x5050a0f0, 0x3c3c7844,
     0x00000000, 0xededc12c, 0x5353a6f5, 0xd1d1b968, 0xb1b179c8, 0x5b5bb6ed, 0x20204060, 0xfcfce31f, 0xbebe67d9, 0x3939724b, 0x6a6ad4be, 0xcbcb8d46, 0x5858b0e8, 0xcfcf854a, 0x4a4a94de, 0x4c4c98d4,
     0x2c2c5874, 0x1a1a342e, 0x0909121b, 0x83831d9e, 0x5a5ab4ee, 0xa0a05bfb, 0x1b1b362d, 0x6e6edcb2, 0xd6d6b761, 0xb3b37dce, 0x5252a4f6, 0x3b3b764d, 0x2f2f5e71, 0x84841397, 0x2929527b, 0xe3e3dd3e,
     0x23234665, 0xc3c39d5e, 0x0404080c, 0xc7c79552, 0x05050a0f, 0x9a9a2fb5, 0x18183028, 0x969637a1, 0x80801b9b, 0xe2e2df3d, 0x07070e09, 0x12122436, 0xb2b27fcd, 0x7575ea9f, 0xebebcd26, 0x27274e69,
     0x93933dae, 0x26264c6a, 0xb7b775c2, 0xfdfde11c, 0xf7f7f502, 0xcccc834f, 0x36366c5a, 0x3f3f7e41, 0xe5e5d134, 0xf1f1f908, 0x3434685c, 0xa5a551f4, 0x31316253, 0x15152a3f, 0x7171e293, 0xd8d8ab73,
     0xc9c98940, 0x7d7dfa87, 0xcaca8f45, 0x82821f9d, 0x47478ec9, 0xf0f0fb0b, 0xfafaef15, 0x5959b2eb, 0xa2a25ffd, 0xafaf45ea, 0xadad41ec, 0xd4d4b367, 0x7272e496, 0xc0c09b5b, 0x9c9c23bf, 0xa4a453f7,
     0x7777ee99, 0x7b7bf68d, 0x6363c6a5, 0x7c7cf884, 0x6f6fdeb1, 0xc5c59154, 0xf2f2ff0d, 0x6b6bd6bd, 0x6767cea9, 0x2b2b567d, 0x30306050, 0x01010203, 0xabab4de6, 0x7676ec9a, 0xfefee719, 0xd7d7b562,
     0x89890980, 0x0d0d1a17, 0x8c8c038f, 0xa1a159f8, 0x424284c6, 0x6868d0b8, 0xbfbf65da, 0xe6e6d731, 0x2d2d5a77, 0x0f0f1e11, 0x414182c3, 0x999929b0, 0xbbbb6dd6, 0x16162c3a, 0xb0b07bcb, 0x5454a8fc,
     0x98982bb3, 0x11112233, 0xe1e1d938, 0xf8f8eb13, 0x8e8e0789, 0x949433a7, 0x6969d2bb, 0xd9d9a970, 0x87871592, 0xe9e9c920, 0x9b9b2db6, 0x1e1e3c22, 0x28285078, 0xdfdfa57a, 0xcece8749, 0x5555aaff,
     0xb5b571c4, 0x6666ccaa, 0x7070e090, 0x3e3e7c42, 0xf6f6f701, 0x0e0e1c12, 0x484890d8, 0x03030605, 0x5757aef9, 0xb9b969d0, 0x6161c2a3, 0x35356a5f, 0x1d1d3a27, 0x9e9e27b9, 0x86861791, 0xc1c19958,
     0x25254a6f, 0x2e2e5c72, 0xbaba6fd5, 0x7878f088, 0xb4b473c7, 0xc6c69751, 0x1c1c3824, 0xa6a657f1, 0x7474e89c, 0x1f1f3e21, 0xe8e8cb23, 0xdddda17c, 0x8b8b0d86, 0x8a8a0f85, 0x4b4b96dd, 0xbdbd61dc,
     0x37376e59, 0x6d6ddab7, 0xe7e7d532, 0xc8c88b43, 0x4e4e9cd2, 0xa9a949e0, 0x8d8d018c, 0xd5d5b164, 0xf4f4f307, 0xeaeacf25, 0x6c6cd8b4, 0x5656acfa, 0xaeae47e9, 0x08081018, 0x6565caaf, 0x7a7af48e,
     0x3a3a744e, 0x0a0a141e, 0xe0e0db3b, 0x32326456, 0x2424486c, 0x5c5cb8e4, 0x494992db, 0x06060c0a, 0xacac43ef, 0x6262c4a6, 0xc2c29f5d, 0xd3d3bd6e, 0xe4e4d337, 0x7979f28b, 0x919139a8, 0x959531a4,
     0x4f4f9ed1, 0xdcdca37f, 0x6060c0a0, 0x81811998, 0x90903bab, 0x88880b83, 0x22224466, 0x2a2a547e, 0xb8b86bd3, 0x1414283c, 0x46468cca, 0xeeeec729, 0x0b0b161d, 0xdbdbad76, 0xdedea779, 0x5e5ebce2,
     0x13132635, 0xececc32f, 0xcdcd814c, 0x0c0c1814, 0x444488cc, 0x17172e39, 0x5f5fbee1, 0x979735a2, 0x7e7efc82, 0x3d3d7a47, 0xc4c49357, 0xa7a755f2, 0x1919322b, 0x7373e695, 0x6464c8ac, 0x5d5dbae7
 ],
 [
     0x3b764d3b, 0x52a4f652, 0xb37dceb3, 0xd6b761d6, 0xe3dd3ee3, 0x29527b29, 0x84139784, 0x2f5e712f, 0x831d9e83, 0x09121b09, 0x1a342e1a, 0x2c58742c, 0x6edcb26e, 0x1b362d1b, 0xa05bfba0, 0x5ab4ee5a,
     0xcb8d46cb, 0x6ad4be6a, 0x39724b39, 0xbe67d9be, 0x4c98d44c, 0x4a94de4a, 0xcf854acf, 0x58b0e858, 0xd1b968d1, 0x53a6f553, 0xedc12ced, 0x00000000, 0xfce31ffc, 0x20406020, 0x5bb6ed5b, 0xb179c8b1,
     0xf9e910f9, 0x458acf45, 0x7ffe817f, 0x02040602, 0x3c78443c, 0x50a0f050, 0xa84be3a8, 0x9f25ba9f, 0xefc52aef, 0xd0bb6bd0, 0xfbed16fb, 0xaa4fe5aa, 0x4d9ad74d, 0x4386c543, 0x85119485, 0x33665533,
     0xb677c1b6, 0xbc63dfbc, 0x21426321, 0xdaaf75da, 0xffe51aff, 0x10203010, 0xd2bf6dd2, 0xf3fd0ef3, 0xa35dfea3, 0x51a2f351, 0x8f058a8f, 0x4080c040, 0x9d21bc9d, 0x923fad92, 0xf5f104f5, 0x38704838,
     0x01020301, 0x30605030, 0x2b567d2b, 0x67cea967, 0xd7b562d7, 0xfee719fe, 0x76ec9a76, 0xab4de6ab, 0x7cf8847c, 0x63c6a563, 0x7bf68d7b, 0x77ee9977, 0x6bd6bd6b, 0xf2ff0df2, 0xc59154c5, 0x6fdeb16f,
     0xd4b367d4, 0xad41ecad, 0xaf45eaaf, 0xa25ffda2, 0xa453f7a4, 0x9c23bf9c, 0xc09b5bc0, 0x72e49672, 0x821f9d82, 0xca8f45ca, 0x7dfa877d, 0xc98940c9, 0x59b2eb59, 0xfaef15fa, 0xf0fb0bf0, 0x478ec947,
     0xa551f4a5, 0x34685c34, 0xf1f908f1, 0xe5d134e5, 0xd8ab73d8, 0x71e29371, 0x152a3f15, 0x31625331, 0xfde11cfd, 0xb775c2b7, 0x264c6a26, 0x933dae93, 0x3f7e413f, 0x366c5a36, 0xcc834fcc, 0xf7f502f7,
     0x12243612, 0x070e0907, 0xe2df3de2, 0x801b9b80, 0x274e6927, 0xebcd26eb, 0x75ea9f75, 0xb27fcdb2, 0xc79552c7, 0x04080c04, 0xc39d5ec3, 0x23466523, 0x9637a196, 0x18302818, 0x9a2fb59a, 0x050a0f05,
     0xdda17cdd, 0xe8cb23e8, 0x1f3e211f, 0x74e89c74, 0xbd61dcbd, 0x4b96dd4b, 0x8a0f858a, 0x8b0d868b, 0x78f08878, 0xba6fd5ba, 0x2e5c722e, 0x254a6f25, 0xa657f1a6, 0x1c38241c, 0xc69751c6, 0xb473c7b4,
     0x356a5f35, 0x61c2a361, 0xb969d0b9, 0x57aef957, 0xc19958c1, 0x86179186, 0x9e27b99e, 0x1d3a271d, 0x3e7c423e, 0x70e09070, 0x66ccaa66, 0xb571c4b5, 0x03060503, 0x4890d848, 0x0e1c120e, 0xf6f701f6,
     0x1e3c221e, 0x9b2db69b, 0xe9c920e9, 0x87159287, 0x55aaff55, 0xce8749ce, 0xdfa57adf, 0x28507828, 0xf8eb13f8, 0xe1d938e1, 0x11223311, 0x982bb398, 0xd9a970d9, 0x69d2bb69, 0x9433a794, 0x8e07898e,
     0x9929b099, 0x4182c341, 0x0f1e110f, 0x2d5a772d, 0x54a8fc54, 0xb07bcbb0, 0x162c3a16, 0xbb6dd6bb, 0xa159f8a1, 0x8c038f8c, 0x0d1a170d, 0x89098089, 0xe6d731e6, 0xbf65dabf, 0x68d0b868, 0x4284c642,
     0xa755f2a7, 0xc49357c4, 0x3d7a473d, 0x7efc827e, 0x5dbae75d, 0x64c8ac64, 0x73e69573, 0x19322b19, 0x0c18140c, 0xcd814ccd, 0xecc32fec, 0x13263513, 0x9735a297, 0x5fbee15f, 0x172e3917, 0x4488cc44,
     0xeec729ee, 0x468cca46, 0x14283c14, 0xb86bd3b8, 0x5ebce25e, 0xdea779de, 0xdbad76db, 0x0b161d0b, 0x81199881, 0x60c0a060, 0xdca37fdc, 0x4f9ed14f, 0x2a547e2a, 0x22446622, 0x880b8388, 0x903bab90,
     0xd3bd6ed3, 0xc29f5dc2, 0x62c4a662, 0xac43efac, 0x9531a495, 0x9139a891, 0x79f28b79, 0xe4d337e4, 0x32645632, 0xe0db3be0, 0x0a141e0a, 0x3a744e3a, 0x060c0a06, 0x4992db49, 0x5cb8e45c, 0x24486c24,
     0x56acfa56, 0x6cd8b46c, 0xeacf25ea, 0xf4f307f4, 0x7af48e7a, 0x65caaf65, 0x08101808, 0xae47e9ae, 0xc88b43c8, 0xe7d532e7, 0x6ddab76d, 0x376e5937, 0xd5b164d5, 0x8d018c8d, 0xa949e0a9, 0x4e9cd24e
 ],
 [
     0x09808989, 0x1a170d0d, 0x038f8c8c, 0x59f8a1a1, 0x84c64242, 0xd0b86868, 0x65dabfbf, 0xd731e6e6, 0x5a772d2d, 0x1e110f0f, 0x82c34141, 0x29b09999, 0x6dd6bbbb, 0x2c3a1616, 0x7bcbb0b0, 0xa8fc5454,
     0x2bb39898, 0x22331111, 0xd938e1e1, 0xeb13f8f8, 0x07898e8e, 0x33a79494, 0xd2bb6969, 0xa970d9d9, 0x15928787, 0xc920e9e9, 0x2db69b9b, 0x3c221e1e, 0x50782828, 0xa57adfdf, 0x8749cece, 0xaaff5555,
     0x71c4b5b5, 0xccaa6666, 0xe0907070, 0x7c423e3e, 0xf701f6f6, 0x1c120e0e, 0x90d84848, 0x06050303, 0xaef95757, 0x69d0b9b9, 0xc2a36161, 0x6a5f3535, 0x3a271d1d, 0x27b99e9e, 0x17918686, 0x9958c1c1,
     0x4a6f2525, 0x5c722e2e, 0x6fd5baba, 0xf0887878, 0x73c7b4b4, 0x9751c6c6, 0x38241c1c, 0x57f1a6a6, 0xe89c7474, 0x3e211f1f, 0xcb23e8e8, 0xa17cdddd, 0x0d868b8b, 0x0f858a8a, 0x96dd4b4b, 0x61dcbdbd,
     0x6e593737, 0xdab76d6d, 0xd532e7e7, 0x8b43c8c8, 0x9cd24e4e, 0x49e0a9a9, 0x018c8d8d, 0xb164d5d5, 0xf307f4f4, 0xcf25eaea, 0xd8b46c6c, 0xacfa5656, 0x47e9aeae, 0x10180808, 0xcaaf6565, 0xf48e7a7a,
     0x744e3a3a, 0x141e0a0a, 0xdb3be0e0, 0x64563232, 0x486c2424, 0xb8e45c5c, 0x92db4949, 0x0c0a0606, 0x43efacac, 0xc4a66262, 0x9f5dc2c2, 0xbd6ed3d3, 0xd337e4e4, 0xf28b7979, 0x39a89191, 0x31a49595,
     0x9ed14f4f, 0xa37fdcdc, 0xc0a06060, 0x19988181, 0x3bab9090, 0x0b838888, 0x44662222, 0x547e2a2a, 0x6bd3b8b8, 0x283c1414, 0x8cca4646, 0xc729eeee, 0x161d0b0b, 0xad76dbdb, 0xa779dede, 0xbce25e5e,
     0x26351313, 0xc32fecec, 0x814ccdcd, 0x18140c0c, 0x88cc4444, 0x2e391717, 0xbee15f5f, 0x35a29797, 0xfc827e7e, 0x7a473d3d, 0x9357c4c4, 0x55f2a7a7, 0x322b1919, 0xe6957373, 0xc8ac6464, 0xbae75d5d,
     0x80c04040, 0x058a8f8f, 0xa2f35151, 0x5dfea3a3, 0x70483838, 0xf104f5f5, 0x3fad9292, 0x21bc9d9d, 0xaf75dada, 0x42632121, 0x63dfbcbc, 0x77c1b6b6, 0xfd0ef3f3, 0xbf6dd2d2, 0x20301010, 0xe51affff,
     0x4fe5aaaa, 0xed16fbfb, 0xbb6bd0d0, 0xc52aefef, 0x66553333, 0x11948585, 0x86c54343, 0x9ad74d4d, 0x04060202, 0xfe817f7f, 0x8acf4545, 0xe910f9f9, 0x25ba9f9f, 0x4be3a8a8, 0xa0f05050, 0x78443c3c,
     0x00000000, 0xc12ceded, 0xa6f55353, 0xb968d1d1, 0x79c8b1b1, 0xb6ed5b5b, 0x40602020, 0xe31ffcfc, 0x67d9bebe, 0x724b3939, 0xd4be6a6a, 0x8d46cbcb, 0xb0e85858, 0x854acfcf, 0x94de4a4a, 0x98d44c4c,
     0x58742c2c, 0x342e1a1a, 0x121b0909, 0x1d9e8383, 0xb4ee5a5a, 0x5bfba0a0, 0x362d1b1b, 0xdcb26e6e, 0xb761d6d6, 0x7dceb3b3, 0xa4f65252, 0x764d3b3b, 0x5e712f2f, 0x13978484, 0x527b2929, 0xdd3ee3e3,
     0x46652323, 0x9d5ec3c3, 0x080c0404, 0x9552c7c7, 0x0a0f0505, 0x2fb59a9a, 0x30281818, 0x37a19696, 0x1b9b8080, 0xdf3de2e2, 0x0e090707, 0x24361212, 0x7fcdb2b2, 0xea9f7575, 0xcd26ebeb, 0x4e692727,
     0x3dae9393, 0x4c6a2626, 0x75c2b7b7, 0xe11cfdfd, 0xf502f7f7, 0x834fcccc, 0x6c5a3636, 0x7e413f3f, 0xd134e5e5, 0xf908f1f1, 0x685c3434, 0x51f4a5a5, 0x62533131, 0x2a3f1515, 0xe2937171, 0xab73d8d8,
     0x8940c9c9, 0xfa877d7d, 0x8f45caca, 0x1f9d8282, 0x8ec94747, 0xfb0bf0f0, 0xef15fafa, 0xb2eb5959, 0x5ffda2a2, 0x45eaafaf, 0x41ecadad, 0xb367d4d4, 0xe4967272, 0x9b5bc0c0, 0x23bf9c9c, 0x53f7a4a4,
     0xee997777, 0xf68d7b7b, 0xc6a56363, 0xf8847c7c, 0xdeb16f6f, 0x9154c5c5, 0xff0df2f2, 0xd6bd6b6b, 0xcea96767, 0x567d2b2b, 0x60503030, 0x02030101, 0x4de6abab, 0xec9a7676, 0xe719fefe, 0xb562d7d7
 ],
 [
     0xc8b1b179, 0xed5b5bb6, 0x60202040, 0x1ffcfce3, 0x00000000, 0x2cededc1, 0xf55353a6, 0x68d1d1b9, 0xe85858b0, 0x4acfcf85, 0xde4a4a94, 0xd44c4c98, 0xd9bebe67, 0x4b393972, 0xbe6a6ad4, 0x46cbcb8d,
     0xee5a5ab4, 0xfba0a05b, 0x2d1b1b36, 0xb26e6edc, 0x742c2c58, 0x2e1a1a34, 0x1b090912, 0x9e83831d, 0x712f2f5e, 0x97848413, 0x7b292952, 0x3ee3e3dd, 0x61d6d6b7, 0xceb3b37d, 0xf65252a4, 0x4d3b3b76,
     0x48383870, 0x04f5f5f1, 0xad92923f, 0xbc9d9d21, 0xc0404080, 0x8a8f8f05, 0xf35151a2, 0xfea3a35d, 0x0ef3f3fd, 0x6dd2d2bf, 0x30101020, 0x1affffe5, 0x75dadaaf, 0x63212142, 0xdfbcbc63, 0xc1b6b677,
     0x55333366, 0x94858511, 0xc5434386, 0xd74d4d9a, 0xe5aaaa4f, 0x16fbfbed, 0x6bd0d0bb, 0x2aefefc5, 0xba9f9f25, 0xe3a8a84b, 0xf05050a0, 0x443c3c78, 0x06020204, 0x817f7ffe, 0xcf45458a, 0x10f9f9e9,
     0xc947478e, 0x0bf0f0fb, 0x15fafaef, 0xeb5959b2, 0x40c9c989, 0x877d7dfa, 0x45caca8f, 0x9d82821f, 0x967272e4, 0x5bc0c09b, 0xbf9c9c23, 0xf7a4a453, 0xfda2a25f, 0xeaafaf45, 0xecadad41, 0x67d4d4b3,
     0xb16f6fde, 0x54c5c591, 0x0df2f2ff, 0xbd6b6bd6, 0x997777ee, 0x8d7b7bf6, 0xa56363c6, 0x847c7cf8, 0xe6abab4d, 0x9a7676ec, 0x19fefee7, 0x62d7d7b5, 0xa96767ce, 0x7d2b2b56, 0x50303060, 0x03010102,
     0x0f05050a, 0xb59a9a2f, 0x28181830, 0xa1969637, 0x65232346, 0x5ec3c39d, 0x0c040408, 0x52c7c795, 0xcdb2b27f, 0x9f7575ea, 0x26ebebcd, 0x6927274e, 0x9b80801b, 0x3de2e2df, 0x0907070e, 0x36121224,
     0x02f7f7f5, 0x4fcccc83, 0x5a36366c, 0x413f3f7e, 0xae93933d, 0x6a26264c, 0xc2b7b775, 0x1cfdfde1, 0x53313162, 0x3f15152a, 0x937171e2, 0x73d8d8ab, 0x34e5e5d1, 0x08f1f1f9, 0x5c343468, 0xf4a5a551,
     0x01f6f6f7, 0x120e0e1c, 0xd8484890, 0x05030306, 0xc4b5b571, 0xaa6666cc, 0x907070e0, 0x423e3e7c, 0x271d1d3a, 0xb99e9e27, 0x91868617, 0x58c1c199, 0xf95757ae, 0xd0b9b969, 0xa36161c2, 0x5f35356a,
     0xc7b4b473, 0x51c6c697, 0x241c1c38, 0xf1a6a657, 0x6f25254a, 0x722e2e5c, 0xd5baba6f, 0x887878f0, 0x868b8b0d, 0x858a8a0f, 0xdd4b4b96, 0xdcbdbd61, 0x9c7474e8, 0x211f1f3e, 0x23e8e8cb, 0x7cdddda1,
     0xc6424284, 0xb86868d0, 0xdabfbf65, 0x31e6e6d7, 0x80898909, 0x170d0d1a, 0x8f8c8c03, 0xf8a1a159, 0xd6bbbb6d, 0x3a16162c, 0xcbb0b07b, 0xfc5454a8, 0x772d2d5a, 0x110f0f1e, 0xc3414182, 0xb0999929,
     0x898e8e07, 0xa7949433, 0xbb6969d2, 0x70d9d9a9, 0xb398982b, 0x33111122, 0x38e1e1d9, 0x13f8f8eb, 0x78282850, 0x7adfdfa5, 0x49cece87, 0xff5555aa, 0x92878715, 0x20e9e9c9, 0xb69b9b2d, 0x221e1e3c,
     0xab90903b, 0x8388880b, 0x66222244, 0x7e2a2a54, 0xd14f4f9e, 0x7fdcdca3, 0xa06060c0, 0x98818119, 0x1d0b0b16, 0x76dbdbad, 0x79dedea7, 0xe25e5ebc, 0xd3b8b86b, 0x3c141428, 0xca46468c, 0x29eeeec7,
     0xcc444488, 0x3917172e, 0xe15f5fbe, 0xa2979735, 0x35131326, 0x2fececc3, 0x4ccdcd81, 0x140c0c18, 0x2b191932, 0x957373e6, 0xac6464c8, 0xe75d5dba, 0x827e7efc, 0x473d3d7a, 0x57c4c493, 0xf2a7a755,
     0xd24e4e9c, 0xe0a9a949, 0x8c8d8d01, 0x64d5d5b1, 0x5937376e, 0xb76d6dda, 0x32e7e7d5, 0x43c8c88b, 0xe9aeae47, 0x18080810, 0xaf6565ca, 0x8e7a7af4, 0x07f4f4f3, 0x25eaeacf, 0xb46c6cd8, 0xfa5656ac,
     0x6c242448, 0xe45c5cb8, 0xdb494992, 0x0a06060c, 0x4e3a3a74, 0x1e0a0a14, 0x3be0e0db, 0x56323264, 0x37e4e4d3, 0x8b7979f2, 0xa8919139, 0xa4959531, 0xefacac43, 0xa66262c4, 0x5dc2c29f, 0x6ed3d3bd
 ],
 [
     0xadad41ec, 0xd4d4b367, 0xa2a25ffd, 0xafaf45ea, 0x9c9c23bf, 0xa4a453f7, 0x7272e496, 0xc0c09b5b, 0xcaca8f45, 0x82821f9d, 0xc9c98940, 0x7d7dfa87, 0xfafaef15, 0x5959b2eb, 0x47478ec9, 0xf0f0fb0b,
     0x30306050, 0x01010203, 0x6767cea9, 0x2b2b567d, 0xfefee719, 0xd7d7b562, 0xabab4de6, 0x7676ec9a, 0x6363c6a5, 0x7c7cf884, 0x7777ee99, 0x7b7bf68d, 0xf2f2ff0d, 0x6b6bd6bd, 0x6f6fdeb1, 0xc5c59154,
     0x07070e09, 0x12122436, 0x80801b9b, 0xe2e2df3d, 0xebebcd26, 0x27274e69, 0xb2b27fcd, 0x7575ea9f, 0x0404080c, 0xc7c79552, 0x23234665, 0xc3c39d5e, 0x18183028, 0x969637a1, 0x05050a0f, 0x9a9a2fb5,
     0x3434685c, 0xa5a551f4, 0xe5e5d134, 0xf1f1f908, 0x7171e293, 0xd8d8ab73, 0x31316253, 0x15152a3f, 0xb7b775c2, 0xfdfde11c, 0x93933dae, 0x26264c6a, 0x36366c5a, 0x3f3f7e41, 0xf7f7f502, 0xcccc834f,
     0x6a6ad4be, 0xcbcb8d46, 0xbebe67d9, 0x3939724b, 0x4a4a94de, 0x4c4c98d4, 0x5858b0e8, 0xcfcf854a, 0x5353a6f5, 0xd1d1b968, 0x00000000, 0xededc12c, 0x20204060, 0xfcfce31f, 0xb1b179c8, 0x5b5bb6ed,
     0x5252a4f6, 0x3b3b764d, 0xd6d6b761, 0xb3b37dce, 0x2929527b, 0xe3e3dd3e, 0x2f2f5e71, 0x84841397, 0x0909121b, 0x83831d9e, 0x2c2c5874, 0x1a1a342e, 0x1b1b362d, 0x6e6edcb2, 0x5a5ab4ee, 0xa0a05bfb,
     0xbcbc63df, 0xb6b677c1, 0xdadaaf75, 0x21214263, 0x10102030, 0xffffe51a, 0xf3f3fd0e, 0xd2d2bf6d, 0x5151a2f3, 0xa3a35dfe, 0x404080c0, 0x8f8f058a, 0x92923fad, 0x9d9d21bc, 0x38387048, 0xf5f5f104,
     0x45458acf, 0xf9f9e910, 0x02020406, 0x7f7ffe81, 0x5050a0f0, 0x3c3c7844, 0x9f9f25ba, 0xa8a84be3, 0xd0d0bb6b, 0xefefc52a, 0xaaaa4fe5, 0xfbfbed16, 0x434386c5, 0x4d4d9ad7, 0x33336655, 0x85851194,
     0x46468cca, 0xeeeec729, 0xb8b86bd3, 0x1414283c, 0xdedea779, 0x5e5ebce2, 0x0b0b161d, 0xdbdbad76, 0x6060c0a0, 0x81811998, 0x4f4f9ed1, 0xdcdca37f, 0x22224466, 0x2a2a547e, 0x90903bab, 0x88880b83,
     0xc4c49357, 0xa7a755f2, 0x7e7efc82, 0x3d3d7a47, 0x6464c8ac, 0x5d5dbae7, 0x1919322b, 0x7373e695, 0xcdcd814c, 0x0c0c1814, 0x13132635, 0xececc32f, 0x5f5fbee1, 0x979735a2, 0x444488cc, 0x17172e39,
     0x6c6cd8b4, 0x5656acfa, 0xf4f4f307, 0xeaeacf25, 0x6565caaf, 0x7a7af48e, 0xaeae47e9, 0x08081018, 0xe7e7d532, 0xc8c88b43, 0x37376e59, 0x6d6ddab7, 0x8d8d018c, 0xd5d5b164, 0x4e4e9cd2, 0xa9a949e0,
     0xc2c29f5d, 0xd3d3bd6e, 0xacac43ef, 0x6262c4a6, 0x919139a8, 0x959531a4, 0xe4e4d337, 0x7979f28b, 0xe0e0db3b, 0x32326456, 0x3a3a744e, 0x0a0a141e, 0x494992db, 0x06060c0a, 0x2424486c, 0x5c5cb8e4,
     0x6161c2a3, 0x35356a5f, 0x5757aef9, 0xb9b969d0, 0x86861791, 0xc1c19958, 0x1d1d3a27, 0x9e9e27b9, 0x7070e090, 0x3e3e7c42, 0xb5b571c4, 0x6666ccaa, 0x484890d8, 0x03030605, 0xf6f6f701, 0x0e0e1c12,
     0xe8e8cb23, 0xdddda17c, 0x7474e89c, 0x1f1f3e21, 0x4b4b96dd, 0xbdbd61dc, 0x8b8b0d86, 0x8a8a0f85, 0xbaba6fd5, 0x7878f088, 0x25254a6f, 0x2e2e5c72, 0x1c1c3824, 0xa6a657f1, 0xb4b473c7, 0xc6c69751,
     0x414182c3, 0x999929b0, 0x2d2d5a77, 0x0f0f1e11, 0xb0b07bcb, 0x5454a8fc, 0xbbbb6dd6, 0x16162c3a, 0x8c8c038f, 0xa1a159f8, 0x89890980, 0x0d0d1a17, 0xbfbf65da, 0xe6e6d731, 0x424284c6, 0x6868d0b8,
     0x9b9b2db6, 0x1e1e3c22, 0x87871592, 0xe9e9c920, 0xcece8749, 0x5555aaff, 0x28285078, 0xdfdfa57a, 0xe1e1d938, 0xf8f8eb13, 0x98982bb3, 0x11112233, 0x6969d2bb, 0xd9d9a970, 0x8e8e0789, 0x949433a7
 ],
 [
     0xdca37fdc, 0x4f9ed14f, 0x81199881, 0x60c0a060, 0x880b8388, 0x903bab90, 0x2a547e2a, 0x22446622, 0x14283c14, 0xb86bd3b8, 0xeec729ee, 0x468cca46, 0xdbad76db, 0x0b161d0b, 0x5ebce25e, 0xdea779de,
     0xecc32fec, 0x13263513, 0x0c18140c, 0xcd814ccd, 0x172e3917, 0x4488cc44, 0x9735a297, 0x5fbee15f, 0x3d7a473d, 0x7efc827e, 0xa755f2a7, 0xc49357c4, 0x73e69573, 0x19322b19, 0x5dbae75d, 0x64c8ac64,
     0x6ddab76d, 0x376e5937, 0xc88b43c8, 0xe7d532e7, 0xa949e0a9, 0x4e9cd24e, 0xd5b164d5, 0x8d018c8d, 0xeacf25ea, 0xf4f307f4, 0x56acfa56, 0x6cd8b46c, 0x08101808, 0xae47e9ae, 0x7af48e7a, 0x65caaf65,
     0x0a141e0a, 0x3a744e3a, 0x32645632, 0xe0db3be0, 0x5cb8e45c, 0x24486c24, 0x060c0a06, 0x4992db49, 0x62c4a662, 0xac43efac, 0xd3bd6ed3, 0xc29f5dc2, 0x79f28b79, 0xe4d337e4, 0x9531a495, 0x9139a891,
     0x66ccaa66, 0xb571c4b5, 0x3e7c423e, 0x70e09070, 0x0e1c120e, 0xf6f701f6, 0x03060503, 0x4890d848, 0xb969d0b9, 0x57aef957, 0x356a5f35, 0x61c2a361, 0x9e27b99e, 0x1d3a271d, 0xc19958c1, 0x86179186,
     0x2e5c722e, 0x254a6f25, 0x78f08878, 0xba6fd5ba, 0xc69751c6, 0xb473c7b4, 0xa657f1a6, 0x1c38241c, 0x1f3e211f, 0x74e89c74, 0xdda17cdd, 0xe8cb23e8, 0x8a0f858a, 0x8b0d868b, 0xbd61dcbd, 0x4b96dd4b,
     0x0d1a170d, 0x89098089, 0xa159f8a1, 0x8c038f8c, 0x68d0b868, 0x4284c642, 0xe6d731e6, 0xbf65dabf, 0x0f1e110f, 0x2d5a772d, 0x9929b099, 0x4182c341, 0x162c3a16, 0xbb6dd6bb, 0x54a8fc54, 0xb07bcbb0,
     0x11223311, 0x982bb398, 0xf8eb13f8, 0xe1d938e1, 0x9433a794, 0x8e07898e, 0xd9a970d9, 0x69d2bb69, 0xe9c920e9, 0x87159287, 0x1e3c221e, 0x9b2db69b, 0xdfa57adf, 0x28507828, 0x55aaff55, 0xce8749ce,
     0x7dfa877d, 0xc98940c9, 0x821f9d82, 0xca8f45ca, 0xf0fb0bf0, 0x478ec947, 0x59b2eb59, 0xfaef15fa, 0xaf45eaaf, 0xa25ffda2, 0xd4b367d4, 0xad41ecad, 0xc09b5bc0, 0x72e49672, 0xa453f7a4, 0x9c23bf9c,
     0x7bf68d7b, 0x77ee9977, 0x7cf8847c, 0x63c6a563, 0xc59154c5, 0x6fdeb16f, 0x6bd6bd6b, 0xf2ff0df2, 0x2b567d2b, 0x67cea967, 0x01020301, 0x30605030, 0x76ec9a76, 0xab4de6ab, 0xd7b562d7, 0xfee719fe,
     0xc39d5ec3, 0x23466523, 0xc79552c7, 0x04080c04, 0x9a2fb59a, 0x050a0f05, 0x9637a196, 0x18302818, 0xe2df3de2, 0x801b9b80, 0x12243612, 0x070e0907, 0x75ea9f75, 0xb27fcdb2, 0x274e6927, 0xebcd26eb,
     0x264c6a26, 0x933dae93, 0xfde11cfd, 0xb775c2b7, 0xcc834fcc, 0xf7f502f7, 0x3f7e413f, 0x366c5a36, 0xf1f908f1, 0xe5d134e5, 0xa551f4a5, 0x34685c34, 0x152a3f15, 0x31625331, 0xd8ab73d8, 0x71e29371,
     0xedc12ced, 0x00000000, 0xd1b968d1, 0x53a6f553, 0x5bb6ed5b, 0xb179c8b1, 0xfce31ffc, 0x20406020, 0x39724b39, 0xbe67d9be, 0xcb8d46cb, 0x6ad4be6a, 0xcf854acf, 0x58b0e858, 0x4c98d44c, 0x4a94de4a,
     0x1a342e1a, 0x2c58742c, 0x831d9e83, 0x09121b09, 0xa05bfba0, 0x5ab4ee5a, 0x6edcb26e, 0x1b362d1b, 0xb37dceb3, 0xd6b761d6, 0x3b764d3b, 0x52a4f652, 0x84139784, 0x2f5e712f, 0xe3dd3ee3, 0x29527b29,
     0x8f058a8f, 0x4080c040, 0xa35dfea3, 0x51a2f351, 0xf5f104f5, 0x38704838, 0x9d21bc9d, 0x923fad92, 0x21426321, 0xdaaf75da, 0xb677c1b6, 0xbc63dfbc, 0xd2bf6dd2, 0xf3fd0ef3, 0xffe51aff, 0x10203010,
     0xfbed16fb, 0xaa4fe5aa, 0xefc52aef, 0xd0bb6bd0, 0x85119485, 0x33665533, 0x4d9ad74d, 0x4386c543, 0x7ffe817f, 0x02040602, 0xf9e910f9, 0x458acf45, 0xa84be3a8, 0x9f25ba9f, 0x3c78443c, 0x50a0f050
 ],
 [
     0x2db69b9b, 0x3c221e1e, 0x15928787, 0xc920e9e9, 0x8749cece, 0xaaff5555, 0x50782828, 0xa57adfdf, 0xd938e1e1, 0xeb13f8f8, 0x2bb39898, 0x22331111, 0xd2bb6969, 0xa970d9d9, 0x07898e8e, 0x33a79494,
     0x82c34141, 0x29b09999, 0x5a772d2d, 0x1e110f0f, 0x7bcbb0b0, 0xa8fc5454, 0x6dd6bbbb, 0x2c3a1616, 0x038f8c8c, 0x59f8a1a1, 0x09808989, 0x1a170d0d, 0x65dabfbf, 0xd731e6e6, 0x84c64242, 0xd0b86868,
     0xcb23e8e8, 0xa17cdddd, 0xe89c7474, 0x3e211f1f, 0x96dd4b4b, 0x61dcbdbd, 0x0d868b8b, 0x0f858a8a, 0x6fd5baba, 0xf0887878, 0x4a6f2525, 0x5c722e2e, 0x38241c1c, 0x57f1a6a6, 0x73c7b4b4, 0x9751c6c6,
     0xc2a36161, 0x6a5f3535, 0xaef95757, 0x69d0b9b9, 0x17918686, 0x9958c1c1, 0x3a271d1d, 0x27b99e9e, 0xe0907070, 0x7c423e3e, 0x71c4b5b5, 0xccaa6666, 0x90d84848, 0x06050303, 0xf701f6f6, 0x1c120e0e,
     0x9f5dc2c2, 0xbd6ed3d3, 0x43efacac, 0xc4a66262, 0x39a89191, 0x31a49595, 0xd337e4e4, 0xf28b7979, 0xdb3be0e0, 0x64563232, 0x744e3a3a, 0x141e0a0a, 0x92db4949, 0x0c0a0606, 0x486c2424, 0xb8e45c5c,
     0xd8b46c6c, 0xacfa5656, 0xf307f4f4, 0xcf25eaea, 0xcaaf6565, 0xf48e7a7a, 0x47e9aeae, 0x10180808, 0xd532e7e7, 0x8b43c8c8, 0x6e593737, 0xdab76d6d, 0x018c8d8d, 0xb164d5d5, 0x9cd24e4e, 0x49e0a9a9,
     0x9357c4c4, 0x55f2a7a7, 0xfc827e7e, 0x7a473d3d, 0xc8ac6464, 0xbae75d5d, 0x322b1919, 0xe6957373, 0x814ccdcd, 0x18140c0c, 0x26351313, 0xc32fecec, 0xbee15f5f, 0x35a29797, 0x88cc4444, 0x2e391717,
     0x8cca4646, 0xc729eeee, 0x6bd3b8b8, 0x283c1414, 0xa779dede, 0xbce25e5e, 0x161d0b0b, 0xad76dbdb, 0xc0a06060, 0x19988181, 0x9ed14f4f, 0xa37fdcdc, 0x44662222, 0x547e2a2a, 0x3bab9090, 0x0b838888,
     0x8acf4545, 0xe910f9f9, 0x04060202, 0xfe817f7f, 0xa0f05050, 0x78443c3c, 0x25ba9f9f, 0x4be3a8a8, 0xbb6bd0d0, 0xc52aefef, 0x4fe5aaaa, 0xed16fbfb, 0x86c54343, 0x9ad74d4d, 0x66553333, 0x11948585,
     0x63dfbcbc, 0x77c1b6b6, 0xaf75dada, 0x42632121, 0x20301010, 0xe51affff, 0xfd0ef3f3, 0xbf6dd2d2, 0xa2f35151, 0x5dfea3a3, 0x80c04040, 0x058a8f8f, 0x3fad9292, 0x21bc9d9d, 0x70483838, 0xf104f5f5,
     0xa4f65252, 0x764d3b3b, 0xb761d6d6, 0x7dceb3b3, 0x527b2929, 0xdd3ee3e3, 0x5e712f2f, 0x13978484, 0x121b0909, 0x1d9e8383, 0x58742c2c, 0x342e1a1a, 0x362d1b1b, 0xdcb26e6e, 0xb4ee5a5a, 0x5bfba0a0,
     0xd4be6a6a, 0x8d46cbcb, 0x67d9bebe, 0x724b3939, 0x94de4a4a, 0x98d44c4c, 0xb0e85858, 0x854acfcf, 0xa6f55353, 0xb968d1d1, 0x00000000, 0xc12ceded, 0x40602020, 0xe31ffcfc, 0x79c8b1b1, 0xb6ed5b5b,
     0x685c3434, 0x51f4a5a5, 0xd134e5e5, 0xf908f1f1, 0xe2937171, 0xab73d8d8, 0x62533131, 0x2a3f1515, 0x75c2b7b7, 0xe11cfdfd, 0x3dae9393, 0x4c6a2626, 0x6c5a3636, 0x7e413f3f, 0xf502f7f7, 0x834fcccc,
     0x0e090707, 0x24361212, 0x1b9b8080, 0xdf3de2e2, 0xcd26ebeb, 0x4e692727, 0x7fcdb2b2, 0xea9f7575, 0x080c0404, 0x9552c7c7, 0x46652323, 0x9d5ec3c3, 0x30281818, 0x37a19696, 0x0a0f0505, 0x2fb59a9a,
     0x60503030, 0x02030101, 0xcea96767, 0x567d2b2b, 0xe719fefe, 0xb562d7d7, 0x4de6abab, 0xec9a7676, 0xc6a56363, 0xf8847c7c, 0xee997777, 0xf68d7b7b, 0xff0df2f2, 0xd6bd6b6b, 0xdeb16f6f, 0x9154c5c5,
     0x41ecadad, 0xb367d4d4, 0x5ffda2a2, 0x45eaafaf, 0x23bf9c9c, 0x53f7a4a4, 0xe4967272, 0x9b5bc0c0, 0x8f45caca, 0x1f9d8282, 0x8940c9c9, 0xfa877d7d, 0xef15fafa, 0xb2eb5959, 0x8ec94747, 0xfb0bf0f0
 ],
 [
     0xdfbcbc63, 0xc1b6b677, 0x75dadaaf, 0x63212142, 0x30101020, 0x1affffe5, 0x0ef3f3fd, 0x6dd2d2bf, 0xf35151a2, 0xfea3a35d, 0xc0404080, 0x8a8f8f05, 0xad92923f, 0xbc9d9d21, 0x48383870, 0x04f5f5f1,
     0xcf45458a, 0x10f9f9e9, 0x06020204, 0x817f7ffe, 0xf05050a0, 0x443c3c78, 0xba9f9f25, 0xe3a8a84b, 0x6bd0d0bb, 0x2aefefc5, 0xe5aaaa4f, 0x16fbfbed, 0xc5434386, 0xd74d4d9a, 0x55333366, 0x94858511,
     0xbe6a6ad4, 0x46cbcb8d, 0xd9bebe67, 0x4b393972, 0xde4a4a94, 0xd44c4c98, 0xe85858b0, 0x4acfcf85, 0xf55353a6, 0x68d1d1b9, 0x00000000, 0x2cededc1, 0x60202040, 0x1ffcfce3, 0xc8b1b179, 0xed5b5bb6,
     0xf65252a4, 0x4d3b3b76, 0x61d6d6b7, 0xceb3b37d, 0x7b292952, 0x3ee3e3dd, 0x712f2f5e, 0x97848413, 0x1b090912, 0x9e83831d, 0x742c2c58, 0x2e1a1a34, 0x2d1b1b36, 0xb26e6edc, 0xee5a5ab4, 0xfba0a05b,
     0x0907070e, 0x36121224, 0x9b80801b, 0x3de2e2df, 0x26ebebcd, 0x6927274e, 0xcdb2b27f, 0x9f7575ea, 0x0c040408, 0x52c7c795, 0x65232346, 0x5ec3c39d, 0x28181830, 0xa1969637, 0x0f05050a, 0xb59a9a2f,
     0x5c343468, 0xf4a5a551, 0x34e5e5d1, 0x08f1f1f9, 0x937171e2, 0x73d8d8ab, 0x53313162, 0x3f15152a, 0xc2b7b775, 0x1cfdfde1, 0xae93933d, 0x6a26264c, 0x5a36366c, 0x413f3f7e, 0x02f7f7f5, 0x4fcccc83,
     0xecadad41, 0x67d4d4b3, 0xfda2a25f, 0xeaafaf45, 0xbf9c9c23, 0xf7a4a453, 0x967272e4, 0x5bc0c09b, 0x45caca8f, 0x9d82821f, 0x40c9c989, 0x877d7dfa, 0x15fafaef, 0xeb5959b2, 0xc947478e, 0x0bf0f0fb,
     0x50303060, 0x03010102, 0xa96767ce, 0x7d2b2b56, 0x19fefee7, 0x62d7d7b5, 0xe6abab4d, 0x9a7676ec, 0xa56363c6, 0x847c7cf8, 0x997777ee, 0x8d7b7bf6, 0x0df2f2ff, 0xbd6b6bd6, 0xb16f6fde, 0x54c5c591,
     0xc3414182, 0xb0999929, 0x772d2d5a, 0x110f0f1e, 0xcbb0b07b, 0xfc5454a8, 0xd6bbbb6d, 0x3a16162c, 0x8f8c8c03, 0xf8a1a159, 0x80898909, 0x170d0d1a, 0xdabfbf65, 0x31e6e6d7, 0xc6424284, 0xb86868d0,
     0xb69b9b2d, 0x221e1e3c, 0x92878715, 0x20e9e9c9, 0x49cece87, 0xff5555aa, 0x78282850, 0x7adfdfa5, 0x38e1e1d9, 0x13f8f8eb, 0xb398982b, 0x33111122, 0xbb6969d2, 0x70d9d9a9, 0x898e8e07, 0xa7949433,
     0xa36161c2, 0x5f35356a, 0xf95757ae, 0xd0b9b969, 0x91868617, 0x58c1c199, 0x271d1d3a, 0xb99e9e27, 0x907070e0, 0x423e3e7c, 0xc4b5b571, 0xaa6666cc, 0xd8484890, 0x05030306, 0x01f6f6f7, 0x120e0e1c,
     0x23e8e8cb, 0x7cdddda1, 0x9c7474e8, 0x211f1f3e, 0xdd4b4b96, 0xdcbdbd61, 0x868b8b0d, 0x858a8a0f, 0xd5baba6f, 0x887878f0, 0x6f25254a, 0x722e2e5c, 0x241c1c38, 0xf1a6a657, 0xc7b4b473, 0x51c6c697,
     0xb46c6cd8, 0xfa5656ac, 0x07f4f4f3, 0x25eaeacf, 0xaf6565ca, 0x8e7a7af4, 0xe9aeae47, 0x18080810, 0x32e7e7d5, 0x43c8c88b, 0x5937376e, 0xb76d6dda, 0x8c8d8d01, 0x64d5d5b1, 0xd24e4e9c, 0xe0a9a949,
     0x5dc2c29f, 0x6ed3d3bd, 0xefacac43, 0xa66262c4, 0xa8919139, 0xa4959531, 0x37e4e4d3, 0x8b7979f2, 0x3be0e0db, 0x56323264, 0x4e3a3a74, 0x1e0a0a14, 0xdb494992, 0x0a06060c, 0x6c242448, 0xe45c5cb8,
     0xca46468c, 0x29eeeec7, 0xd3b8b86b, 0x3c141428, 0x79dedea7, 0xe25e5ebc, 0x1d0b0b16, 0x76dbdbad, 0xa06060c0, 0x98818119, 0xd14f4f9e, 0x7fdcdca3, 0x66222244, 0x7e2a2a54, 0xab90903b, 0x8388880b,
     0x57c4c493, 0xf2a7a755, 0x827e7efc, 0x473d3d7a, 0xac6464c8, 0xe75d5dba, 0x2b191932, 0x957373e6, 0x4ccdcd81, 0x140c0c18, 0x35131326, 0x2fececc3, 0xe15f5fbe, 0xa2979735, 0xcc444488, 0x3917172e
 ],
 [
     0x3434685c, 0xa5a551f4, 0xe5e5d134, 0xf1f1f908, 0x7171e293, 0xd8d8ab73, 0x31316253, 0x15152a3f, 0xb7b775c2, 0xfdfde11c, 0x93933dae, 0x26264c6a, 0x36366c5a, 0x3f3f7e41, 0xf7f7f502, 0xcccc834f,
     0x07070e09, 0x12122436, 0x80801b9b, 0xe2e2df3d, 0xebebcd26, 0x27274e69, 0xb2b27fcd, 0x7575ea9f, 0x0404080c, 0xc7c79552, 0x23234665, 0xc3c39d5e, 0x18183028, 0x969637a1, 0x05050a0f, 0x9a9a2fb5,
     0x30306050, 0x01010203, 0x6767cea9, 0x2b2b567d, 0xfefee719, 0xd7d7b562, 0xabab4de6, 0x7676ec9a, 0x6363c6a5, 0x7c7cf884, 0x7777ee99, 0x7b7bf68d, 0xf2f2ff0d, 0x6b6bd6bd, 0x6f6fdeb1, 0xc5c59154,
     0xadad41ec, 0xd4d4b367, 0xa2a25ffd, 0xafaf45ea, 0x9c9c23bf, 0xa4a453f7, 0x7272e496, 0xc0c09b5b, 0xcaca8f45, 0x82821f9d, 0xc9c98940, 0x7d7dfa87, 0xfafaef15, 0x5959b2eb, 0x47478ec9, 0xf0f0fb0b,
     0x45458acf, 0xf9f9e910, 0x02020406, 0x7f7ffe81, 0x5050a0f0, 0x3c3c7844, 0x9f9f25ba, 0xa8a84be3, 0xd0d0bb6b, 0xefefc52a, 0xaaaa4fe5, 0xfbfbed16, 0x434386c5, 0x4d4d9ad7, 0x33336655, 0x85851194,
     0xbcbc63df, 0xb6b677c1, 0xdadaaf75, 0x21214263, 0x10102030, 0xffffe51a, 0xf3f3fd0e, 0xd2d2bf6d, 0x5151a2f3, 0xa3a35dfe, 0x404080c0, 0x8f8f058a, 0x92923fad, 0x9d9d21bc, 0x38387048, 0xf5f5f104,
     0x5252a4f6, 0x3b3b764d, 0xd6d6b761, 0xb3b37dce, 0x2929527b, 0xe3e3dd3e, 0x2f2f5e71, 0x84841397, 0x0909121b, 0x83831d9e, 0x2c2c5874, 0x1a1a342e, 0x1b1b362d, 0x6e6edcb2, 0x5a5ab4ee, 0xa0a05bfb,
     0x6a6ad4be, 0xcbcb8d46, 0xbebe67d9, 0x3939724b, 0x4a4a94de, 0x4c4c98d4, 0x5858b0e8, 0xcfcf854a, 0x5353a6f5, 0xd1d1b968, 0x00000000, 0xededc12c, 0x20204060, 0xfcfce31f, 0xb1b179c8, 0x5b5bb6ed,
     0xc2c29f5d, 0xd3d3bd6e, 0xacac43ef, 0x6262c4a6, 0x919139a8, 0x959531a4, 0xe4e4d337, 0x7979f28b, 0xe0e0db3b, 0x32326456, 0x3a3a744e, 0x0a0a141e, 0x494992db, 0x06060c0a, 0x2424486c, 0x5c5cb8e4,
     0x6c6cd8b4, 0x5656acfa, 0xf4f4f307, 0xeaeacf25, 0x6565caaf, 0x7a7af48e, 0xaeae47e9, 0x08081018, 0xe7e7d532, 0xc8c88b43, 0x37376e59, 0x6d6ddab7, 0x8d8d018c, 0xd5d5b164, 0x4e4e9cd2, 0xa9a949e0,
     0xc4c49357, 0xa7a755f2, 0x7e7efc82, 0x3d3d7a47, 0x6464c8ac, 0x5d5dbae7, 0x1919322b, 0x7373e695, 0xcdcd814c, 0x0c0c1814, 0x13132635, 0xececc32f, 0x5f5fbee1, 0x979735a2, 0x444488cc, 0x17172e39,
     0x46468cca, 0xeeeec729, 0xb8b86bd3, 0x1414283c, 0xdedea779, 0x5e5ebce2, 0x0b0b161d, 0xdbdbad76, 0x6060c0a0, 0x81811998, 0x4f4f9ed1, 0xdcdca37f, 0x22224466, 0x2a2a547e, 0x90903bab, 0x88880b83,
     0x9b9b2db6, 0x1e1e3c22, 0x87871592, 0xe9e9c920, 0xcece8749, 0x5555aaff, 0x28285078, 0xdfdfa57a, 0xe1e1d938, 0xf8f8eb13, 0x98982bb3, 0x11112233, 0x6969d2bb, 0xd9d9a970, 0x8e8e0789, 0x949433a7,
     0x414182c3, 0x999929b0, 0x2d2d5a77, 0x0f0f1e11, 0xb0b07bcb, 0x5454a8fc, 0xbbbb6dd6, 0x16162c3a, 0x8c8c038f, 0xa1a159f8, 0x89890980, 0x0d0d1a17, 0xbfbf65da, 0xe6e6d731, 0x424284c6, 0x6868d0b8,
     0xe8e8cb23, 0xdddda17c, 0x7474e89c, 0x1f1f3e21, 0x4b4b96dd, 0xbdbd61dc, 0x8b8b0d86, 0x8a8a0f85, 0xbaba6fd5, 0x7878f088, 0x25254a6f, 0x2e2e5c72, 0x1c1c3824, 0xa6a657f1, 0xb4b473c7, 0xc6c69751,
     0x6161c2a3, 0x35356a5f, 0x5757aef9, 0xb9b969d0, 0x86861791, 0xc1c19958, 0x1d1d3a27, 0x9e9e27b9, 0x7070e090, 0x3e3e7c42, 0xb5b571c4, 0x6666ccaa, 0x484890d8, 0x03030605, 0xf6f6f701, 0x0e0e1c12
 ],
 [
     0x9735a297, 0x5fbee15f, 0x172e3917, 0x4488cc44, 0x0c18140c, 0xcd814ccd, 0xecc32fec, 0x13263513, 0x5dbae75d, 0x64c8ac64, 0x73e69573, 0x19322b19, 0xa755f2a7, 0xc49357c4, 0x3d7a473d, 0x7efc827e,
     0x2a547e2a, 0x22446622, 0x880b8388, 0x903bab90, 0x81199881, 0x60c0a060, 0xdca37fdc, 0x4f9ed14f, 0x5ebce25e, 0xdea779de, 0xdbad76db, 0x0b161d0b, 0xeec729ee, 0x468cca46, 0x14283c14, 0xb86bd3b8,
     0x060c0a06, 0x4992db49, 0x5cb8e45c, 0x24486c24, 0x32645632, 0xe0db3be0, 0x0a141e0a, 0x3a744e3a, 0x9531a495, 0x9139a891, 0x79f28b79, 0xe4d337e4, 0xd3bd6ed3, 0xc29f5dc2, 0x62c4a662, 0xac43efac,
     0xd5b164d5, 0x8d018c8d, 0xa949e0a9, 0x4e9cd24e, 0xc88b43c8, 0xe7d532e7, 0x6ddab76d, 0x376e5937, 0x7af48e7a, 0x65caaf65, 0x08101808, 0xae47e9ae, 0x56acfa56, 0x6cd8b46c, 0xeacf25ea, 0xf4f307f4,
     0xa657f1a6, 0x1c38241c, 0xc69751c6, 0xb473c7b4, 0x78f08878, 0xba6fd5ba, 0x2e5c722e, 0x254a6f25, 0xbd61dcbd, 0x4b96dd4b, 0x8a0f858a, 0x8b0d868b, 0xdda17cdd, 0xe8cb23e8, 0x1f3e211f, 0x74e89c74,
     0x03060503, 0x4890d848, 0x0e1c120e, 0xf6f701f6, 0x3e7c423e, 0x70e09070, 0x66ccaa66, 0xb571c4b5, 0xc19958c1, 0x86179186, 0x9e27b99e, 0x1d3a271d, 0x356a5f35, 0x61c2a361, 0xb969d0b9, 0x57aef957,
     0xd9a970d9, 0x69d2bb69, 0x9433a794, 0x8e07898e, 0xf8eb13f8, 0xe1d938e1, 0x11223311, 0x982bb398, 0x55aaff55, 0xce8749ce, 0xdfa57adf, 0x28507828, 0x1e3c221e, 0x9b2db69b, 0xe9c920e9, 0x87159287,
     0xe6d731e6, 0xbf65dabf, 0x68d0b868, 0x4284c642, 0xa159f8a1, 0x8c038f8c, 0x0d1a170d, 0x89098089, 0x54a8fc54, 0xb07bcbb0, 0x162c3a16, 0xbb6dd6bb, 0x9929b099, 0x4182c341, 0x0f1e110f, 0x2d5a772d,
     0x6bd6bd6b, 0xf2ff0df2, 0xc59154c5, 0x6fdeb16f, 0x7cf8847c, 0x63c6a563, 0x7bf68d7b, 0x77ee9977, 0xd7b562d7, 0xfee719fe, 0x76ec9a76, 0xab4de6ab, 0x01020301, 0x30605030, 0x2b567d2b, 0x67cea967,
     0x59b2eb59, 0xfaef15fa, 0xf0fb0bf0, 0x478ec947, 0x821f9d82, 0xca8f45ca, 0x7dfa877d, 0xc98940c9, 0xa453f7a4, 0x9c23bf9c, 0xc09b5bc0, 0x72e49672, 0xd4b367d4, 0xad41ecad, 0xaf45eaaf, 0xa25ffda2,
     0x3f7e413f, 0x366c5a36, 0xcc834fcc, 0xf7f502f7, 0xfde11cfd, 0xb775c2b7, 0x264c6a26, 0x933dae93, 0xd8ab73d8, 0x71e29371, 0x152a3f15, 0x31625331, 0xa551f4a5, 0x34685c34, 0xf1f908f1, 0xe5d134e5,
     0x9637a196, 0x18302818, 0x9a2fb59a, 0x050a0f05, 0xc79552c7, 0x04080c04, 0xc39d5ec3, 0x23466523, 0x274e6927, 0xebcd26eb, 0x75ea9f75, 0xb27fcdb2, 0x12243612, 0x070e0907, 0xe2df3de2, 0x801b9b80,
     0x6edcb26e, 0x1b362d1b, 0xa05bfba0, 0x5ab4ee5a, 0x831d9e83, 0x09121b09, 0x1a342e1a, 0x2c58742c, 0xe3dd3ee3, 0x29527b29, 0x84139784, 0x2f5e712f, 0x3b764d3b, 0x52a4f652, 0xb37dceb3, 0xd6b761d6,
     0xfce31ffc, 0x20406020, 0x5bb6ed5b, 0xb179c8b1, 0xd1b968d1, 0x53a6f553, 0xedc12ced, 0x00000000, 0x4c98d44c, 0x4a94de4a, 0xcf854acf, 0x58b0e858, 0xcb8d46cb, 0x6ad4be6a, 0x39724b39, 0xbe67d9be,
     0x4d9ad74d, 0x4386c543, 0x85119485, 0x33665533, 0xefc52aef, 0xd0bb6bd0, 0xfbed16fb, 0xaa4fe5aa, 0x3c78443c, 0x50a0f050, 0xa84be3a8, 0x9f25ba9f, 0xf9e910f9, 0x458acf45, 0x7ffe817f, 0x02040602,
     0x9d21bc9d, 0x923fad92, 0xf5f104f5, 0x38704838, 0xa35dfea3, 0x51a2f351, 0x8f058a8f, 0x4080c040, 0xffe51aff, 0x10203010, 0xd2bf6dd2, 0xf3fd0ef3, 0xb677c1b6, 0xbc63dfbc, 0x21426321, 0xdaaf75da
 ],
 [
     0x3e211f1f, 0xe89c7474, 0xa17cdddd, 0xcb23e8e8, 0x0f858a8a, 0x0d868b8b, 0x61dcbdbd, 0x96dd4b4b, 0x5c722e2e, 0x4a6f2525, 0xf0887878, 0x6fd5baba, 0x9751c6c6, 0x73c7b4b4, 0x57f1a6a6, 0x38241c1c,
     0x69d0b9b9, 0xaef95757, 0x6a5f3535, 0xc2a36161, 0x27b99e9e, 0x3a271d1d, 0x9958c1c1, 0x17918686, 0xccaa6666, 0x71c4b5b5, 0x7c423e3e, 0xe0907070, 0x1c120e0e, 0xf701f6f6, 0x06050303, 0x90d84848,
     0xc920e9e9, 0x15928787, 0x3c221e1e, 0x2db69b9b, 0xa57adfdf, 0x50782828, 0xaaff5555, 0x8749cece, 0x22331111, 0x2bb39898, 0xeb13f8f8, 0xd938e1e1, 0x33a79494, 0x07898e8e, 0xa970d9d9, 0xd2bb6969,
     0x1e110f0f, 0x5a772d2d, 0x29b09999, 0x82c34141, 0x2c3a1616, 0x6dd6bbbb, 0xa8fc5454, 0x7bcbb0b0, 0x1a170d0d, 0x09808989, 0x59f8a1a1, 0x038f8c8c, 0xd0b86868, 0x84c64242, 0xd731e6e6, 0x65dabfbf,
     0x7a473d3d, 0xfc827e7e, 0x55f2a7a7, 0x9357c4c4, 0xe6957373, 0x322b1919, 0xbae75d5d, 0xc8ac6464, 0xc32fecec, 0x26351313, 0x18140c0c, 0x814ccdcd, 0x2e391717, 0x88cc4444, 0x35a29797, 0xbee15f5f,
     0x283c1414, 0x6bd3b8b8, 0xc729eeee, 0x8cca4646, 0xad76dbdb, 0x161d0b0b, 0xbce25e5e, 0xa779dede, 0xa37fdcdc, 0x9ed14f4f, 0x19988181, 0xc0a06060, 0x0b838888, 0x3bab9090, 0x547e2a2a, 0x44662222,
     0xc4a66262, 0x43efacac, 0xbd6ed3d3, 0x9f5dc2c2, 0xf28b7979, 0xd337e4e4, 0x31a49595, 0x39a89191, 0x141e0a0a, 0x744e3a3a, 0x64563232, 0xdb3be0e0, 0xb8e45c5c, 0x486c2424, 0x0c0a0606, 0x92db4949,
     0xcf25eaea, 0xf307f4f4, 0xacfa5656, 0xd8b46c6c, 0x10180808, 0x47e9aeae, 0xf48e7a7a, 0xcaaf6565, 0xdab76d6d, 0x6e593737, 0x8b43c8c8, 0xd532e7e7, 0x49e0a9a9, 0x9cd24e4e, 0xb164d5d5, 0x018c8d8d,
     0x7dceb3b3, 0xb761d6d6, 0x764d3b3b, 0xa4f65252, 0x13978484, 0x5e712f2f, 0xdd3ee3e3, 0x527b2929, 0x342e1a1a, 0x58742c2c, 0x1d9e8383, 0x121b0909, 0x5bfba0a0, 0xb4ee5a5a, 0xdcb26e6e, 0x362d1b1b,
     0x724b3939, 0x67d9bebe, 0x8d46cbcb, 0xd4be6a6a, 0x854acfcf, 0xb0e85858, 0x98d44c4c, 0x94de4a4a, 0xc12ceded, 0x00000000, 0xb968d1d1, 0xa6f55353, 0xb6ed5b5b, 0x79c8b1b1, 0xe31ffcfc, 0x40602020,
     0xfe817f7f, 0x04060202, 0xe910f9f9, 0x8acf4545, 0x4be3a8a8, 0x25ba9f9f, 0x78443c3c, 0xa0f05050, 0xed16fbfb, 0x4fe5aaaa, 0xc52aefef, 0xbb6bd0d0, 0x11948585, 0x66553333, 0x9ad74d4d, 0x86c54343,
     0x42632121, 0xaf75dada, 0x77c1b6b6, 0x63dfbcbc, 0xbf6dd2d2, 0xfd0ef3f3, 0xe51affff, 0x20301010, 0x058a8f8f, 0x80c04040, 0x5dfea3a3, 0xa2f35151, 0xf104f5f5, 0x70483838, 0x21bc9d9d, 0x3fad9292,
     0x567d2b2b, 0xcea96767, 0x02030101, 0x60503030, 0xec9a7676, 0x4de6abab, 0xb562d7d7, 0xe719fefe, 0xf68d7b7b, 0xee997777, 0xf8847c7c, 0xc6a56363, 0x9154c5c5, 0xdeb16f6f, 0xd6bd6b6b, 0xff0df2f2,
     0x45eaafaf, 0x5ffda2a2, 0xb367d4d4, 0x41ecadad, 0x9b5bc0c0, 0xe4967272, 0x53f7a4a4, 0x23bf9c9c, 0xfa877d7d, 0x8940c9c9, 0x1f9d8282, 0x8f45caca, 0xfb0bf0f0, 0x8ec94747, 0xb2eb5959, 0xef15fafa,
     0xf908f1f1, 0xd134e5e5, 0x51f4a5a5, 0x685c3434, 0x2a3f1515, 0x62533131, 0xab73d8d8, 0xe2937171, 0x4c6a2626, 0x3dae9393, 0xe11cfdfd, 0x75c2b7b7, 0x834fcccc, 0xf502f7f7, 0x7e413f3f, 0x6c5a3636,
     0xdf3de2e2, 0x1b9b8080, 0x24361212, 0x0e090707, 0xea9f7575, 0x7fcdb2b2, 0x4e692727, 0xcd26ebeb, 0x9d5ec3c3, 0x46652323, 0x9552c7c7, 0x080c0404, 0x2fb59a9a, 0x0a0f0505, 0x37a19696, 0x30281818
 ]
]

secretKey = [0 for _ in range(16)]
MixColumnLUT = [[0 for col in range(256)] for row in range(4)]

for i in range(0,4):
 for j in range(0,256):
  t = [0 for _ in range(4)]
  t[3] = format(gmul[matrix_4x4[i + 0]][j],'02x')
  t[2]=  format(gmul[matrix_4x4[i + 4]][j],'02x')
  t[1] = format(gmul[matrix_4x4[i + 8]][j],'02x')
  t[0] = format(gmul[matrix_4x4[i + 12]][j],'02x')
  x = "".join(x for x in t)
  MixColumnLUT[i][j]=x

for i in range(0,16):
 M_TBoxesKey= format(M_TBoxesR0[i][0],'08x')
 for j in range(0,256):
  keyOffset = Sbox[j]
  gussedKey = MixColumnLUT[i % 4][keyOffset]
  if (M_TBoxesKey==gussedKey):
   secretKey[i]=j

"""  
    ḱ is the result of applying ShiftRows to the round key 
    Therefore, To get the secretKey you need to unShiftRow.

    unShiftRows
    +----+----+----+----+  
    | 00 | 04 | 08 | 12 |
    +----+----+----+----+
    | 01 | 05 | 09 | 13 | 
    +----+----+----+----+ 
    | 02 | 06 | 10 | 14 |
    +----+----+----+----+
    | 03 | 07 | 11 | 15 |
    +----+----+----+----+
"""
for i in range(1,4):
 s=0
 while(s<i):
  tmp = secretKey[i+12]
  for k in range(2,-1,-1):
   secretKey[k*4+i+4]=secretKey[k*4+i]
  secretKey[i]=tmp
  s=s+1

secretKey = "".join(hex(x)[2:] for x in secretKey)
print "secretKey:"+ secretKey.upper()
secretKey = binascii.unhexlify(secretKey)

#decrypt Flag and print
flag = base64.b64decode(encFlag)
cipher = AES.new(secretKey, AES.MODE_ECB)
flag = cipher.decrypt(flag)
print "deryptedFlag:"+ flag


h2spices-MacBook-Pro:Seccon2016_Crypto500_OAES h2spice$ python exploit_Crypto500.py
encryptedFlag:g1UlZafiuGdCgpTkWYjaZg3kE6qCd7kF3kV+nMKcGHc=
secretKey:6C2893F21B6185E8567238CB78184945
deryptedFlag:SECCON{owSkwPeH1CHQdPV9KWrSmz9n}

ありがとうございます お疲れ様でした。