import hashlib
from sage.all import *

def gen_pubkey(secret: bytes, hasher=hashlib.SHA512) -> list:
    def hash(m): return hasher(m).digest()
    state = hash(secret)
    pubkey = []
    for _ in range(len(hash(b'0')) * 4):
        pubkey.append(int.from_bytes(state, 'big'))
        state = hash(state)
    return pubkey


def happiness(x: int) -> int:
    return x - sum((x >> i) for i in range(1, x.bit_length()))


def encode_message(message: bytes, segment_len: int) -> list:
    message += bytes(segment_len - len(message) % (segment_len))
    encoded = []
    for i in range(0, len(message), segment_len):
        block = message[i:i + segment_len]
        encoded.append(int.from_bytes(block, 'big'))
    return encoded


def encrypt(pubkey: list, message: bytes) -> list:
    encrypted_blocks = []
    for block_int in encode_message(message, len(pubkey) // 4):
        encrypted_blocks.append([happiness(i & block_int) for i in pubkey])
    return encrypted_blocks

secret1 = bytes.fromhex("2329d5d8515229084589a6570919558f")
secret2 = bytes.fromhex("5a57b559987fb0f351f73647228e74fb")
enc2 = [[83, 67, 72, 64, 79, 69, 69, 76, 67, 60, 89, 60, 69, 74, 57, 77, 65, 77, 57, 67, 69, 61, 73, 64, 70, 73, 76, 51, 72, 74, 69, 68, 65, 69, 74, 70, 78, 56, 79, 57, 79, 72, 66, 81, 74, 78, 71, 68, 80, 58, 72, 79, 76, 78, 70, 76, 66, 66, 73, 70, 67, 62, 75, 77, 57, 70, 63, 66, 59, 68, 69, 70, 62, 72, 69, 76, 56, 67, 73, 66, 66, 76, 73, 62, 71, 68, 82, 75, 70, 75, 64, 67, 68, 63, 72, 71, 70, 60, 74, 72, 61, 75, 69, 71, 62, 74, 70, 71, 70, 82, 61, 75, 72, 62, 80, 67, 72, 63, 67, 71, 67, 68, 65, 72, 70, 68, 77, 64], [73, 68, 66, 74, 76, 72, 66, 71, 68, 57, 75, 59, 66, 68, 63, 73, 60, 62, 62, 65, 72, 57, 72, 63, 75, 71, 71, 54, 64, 73, 67, 65, 60, 69, 72, 70, 79, 62, 63, 64, 73, 63, 63, 80, 76, 78, 74, 65, 73, 63, 79, 81, 74, 76, 62, 73, 73, 64, 62, 74, 68, 55, 78, 63, 65, 65, 63, 64, 61, 73, 73, 65, 67, 67, 69, 69, 61, 66, 68, 66, 70, 66, 68, 57, 71, 64, 79, 71, 62, 77, 63, 61, 67, 62, 69, 61, 74, 57, 68, 63, 69, 76, 67, 74, 54, 73, 70, 65, 71, 77, 58, 76, 62, 69, 73, 58, 67, 65, 64, 65, 70, 73, 67, 72, 66, 59, 67, 73], [34, 35, 27, 29, 30, 34, 27, 32, 34, 30, 36, 34, 27, 30, 23, 27, 29, 32, 27, 28, 33, 21, 35, 24, 26, 36, 34, 24, 23, 27, 32, 37, 31, 27, 33, 31, 25, 30, 28, 26, 39, 29, 30, 30, 40, 35, 29, 31, 28, 27, 33, 40, 25, 33, 30, 34, 24, 26, 28, 30, 25, 31, 35, 32, 23, 33, 25, 32, 26, 32, 36, 28, 28, 31, 27, 29, 27, 35, 29, 31, 30, 26, 25, 29, 30, 25, 39, 28, 31, 28, 24, 33, 31, 32, 29, 22, 34, 23, 28, 31, 31, 33, 33, 33, 28, 32, 31, 32, 38, 33, 25, 31, 34, 28, 32, 27, 31, 30, 32, 33, 27, 25, 32, 37, 32, 26, 38, 27]]
enc1 = [[63, 67, 73, 73, 63, 62, 67, 72, 75, 73, 71, 75, 67, 65, 71, 68, 84, 67, 67, 69, 67, 65, 78, 71, 68, 74, 67, 69, 74, 59, 71, 70, 66, 73, 75, 72, 76, 61, 60, 67, 70, 70, 73, 63, 62, 75, 74, 77, 72, 56, 72, 77, 68, 77, 74, 79, 73, 77, 72, 63, 67, 77, 72, 82, 78, 69, 60, 74, 61, 71, 57, 65, 64, 77, 69, 60, 69, 61, 75, 61, 65, 71, 75, 70, 77, 69, 66, 74, 70, 78, 62, 73, 67, 72, 75, 78, 73, 70, 62, 72, 67, 61, 63, 69, 83, 75, 67, 84, 62, 70, 72, 67, 65, 66, 65, 73, 80, 69, 67, 71, 67, 65, 69, 79, 69, 59, 70, 71], [54, 70, 68, 69, 62, 65, 60, 75, 82, 73, 68, 73, 65, 60, 73, 71, 71, 71, 66, 69, 66, 66, 72, 67, 63, 80, 61, 67, 71, 65, 70, 73, 64, 68, 72, 73, 75, 60, 64, 70, 71, 70, 72, 61, 64, 64, 75, 69, 72, 63, 67, 72, 64, 71, 78, 74, 65, 71, 72, 61, 75, 71, 69, 77, 79, 69, 55, 63, 58, 63, 67, 73, 70, 72, 63, 59, 66, 63, 78, 63, 62, 67, 80, 67, 75, 70, 70, 71, 73, 71, 65, 72, 67, 58, 77, 69, 64, 62, 61, 70, 66, 52, 57, 68, 85, 73, 72, 75, 63, 69, 69, 70, 59, 76, 62, 64, 80, 64, 68, 77, 65, 50, 69, 76, 79, 52, 71, 73], [25, 32, 34, 38, 28, 33, 20, 35, 38, 27, 25, 32, 26, 29, 26, 28, 29, 31, 30, 28, 32, 29, 37, 31, 29, 39, 27, 28, 28, 24, 34, 37, 25, 35, 28, 37, 39, 24, 28, 26, 33, 26, 33, 21, 28, 31, 29, 28, 24, 22, 32, 32, 31, 32, 36, 32, 24, 34, 32, 28, 32, 38, 34, 31, 35, 28, 25, 29, 27, 26, 35, 28, 32, 31, 30, 23, 28, 21, 32, 26, 30, 28, 28, 28, 34, 23, 23, 29, 35, 29, 32, 29, 36, 32, 31, 32, 25, 28, 26, 30, 27, 23, 23, 32, 36, 30, 24, 34, 25, 30, 29, 30, 24, 31, 27, 33, 28, 25, 27, 28, 30, 21, 28, 24, 31, 20, 33, 32]]

pubkey1 = gen_pubkey(secret1, hashlib.SHA256)
pubkey2 = gen_pubkey(secret2, hashlib.SHA256)
mat = []

# print(len(pubkey), pubkey[0].bit_length())
for pub in pubkey1:
    m = list(map(int, bin(pub)[2:].zfill(256)))
    mat.append(m)
for pub in pubkey2:
    m = list(map(int, bin(pub)[2:].zfill(256)))
    mat.append(m)
    
F = ZZ
mat = matrix(F, mat)
flag = b""
for i in range(3):
    msg = mat.inverse() * vector(F, enc1[i] + enc2[i])
    msg = ''.join(list(map(str, msg)))
    flag += int.to_bytes(int(msg, 2), 32, 'big')
print(flag)

# b'SEKAI{w3ll_1_gu355_y0u_c4n_4lw4y5_4sk_f0r_m0r3_3qu4t10n5_wh3n_n0_0n3s_l00k1ng}\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00'