sha_256 1.0.1

#![no_std]

use core::convert::TryInto;
use core::iter::Iterator;

/// A structure representing the SHA-256 hash algorithm.
pub struct Sha256 {
    w: [u32; 64], // words for the message schedule
    // the 8 hash values
    h0: u32,
    h1: u32,
    h2: u32,
    h3: u32,
    h4: u32,
    h5: u32,
    h6: u32,
    h7: u32,
}

impl Default for Sha256 {
    fn default() -> Self {
        Self::new()
    }
}

impl Sha256 {
    /// Creates a new instance of the SHA-256 hash algorithm.
    ///
    /// # Returns
    /// A new `Sha256` instance with initialized state.
    pub fn new() -> Self {
        Self {
            w: [0; 64],
            h0: 0,
            h1: 0,
            h2: 0,
            h3: 0,
            h4: 0,
            h5: 0,
            h6: 0,
            h7: 0,
        }
    }

    /// Sets a chunk of the message for SHA-256 processing.
    ///
    /// # Arguments
    /// * `msg` - A byte slice representing the message to be hashed.
    /// * `index` - The index of the chunk to be set.
    #[inline(always)]
    fn set_chunk(&mut self, msg: &[u8], index: usize) {
        unsafe {
            // message entirely saturates this chunk, so straight-up copy the bytes into u32's
            let start = index * 64;
            let end = start + 64;
            let slice = &msg[start..end];
            for (i, chunk) in slice.chunks_exact(4).enumerate() {
                self.w[i] = u32::from_be_bytes(chunk.try_into().unwrap());
            }
        }
    }

    #[inline(always)]
    fn set_chunk_last(&mut self, msg: &[u8], index: usize) {
        // copy the remaining msg into the w array
        let msg_len = msg.len();
        let start = index * 64;
        let n_u32s = (msg_len - start) / 4; // how many 4 byte blocks are in the remaining message
        let n_rem_bytes = msg_len % 4; // how many leftover bytes are in the remaining message after the 4 byte blocks
        let end_u32s = msg_len - n_rem_bytes;
        // for every 4 byte chunk in the remaining message
        let slice = &msg[start..end_u32s];
        for (i, chunk) in slice.chunks_exact(4).enumerate() {
            // convert the 4 byte chunk into a u32 and store it in the w array
            self.w[i] = u32::from_be_bytes(chunk.try_into().unwrap());
        }
        
        // there will be 0-3 bytes left over which didn't fit into the 4 byte chunks
        // copy these into a 4 byte chunk
        let mut bytes = [0u8; 4];
        let slice_rem = &msg[end_u32s..];
        bytes[0..n_rem_bytes].copy_from_slice(slice_rem);
        // after the msg ends, we pad with a 0b10000000 byte
        bytes[n_rem_bytes] = 0b10000000;
        // convert the bytes into a u32
        self.w[n_u32s] = u32::from_be_bytes(bytes);

        // any u32s after the message but before the last 2 u32s are 0
        let i = n_u32s + 1;
        self.set_chunk_padding_zeros(msg, i);

        // if the message length is <=55 bytes and >=1 byte, the padding will fit into the last chunk
        // a message of <=55 bytes will have space for the length field in this chunk
        // 55 bytes of message + 1 byte of padding = 56 bytes = 14 u32s
        // length field goes in w[14] and w[15]
        if i <= 14 {
            // space for length field
            // remaining message fits into the last chunk with padding included.
            self.set_chunk_msg_len(msg);
        } else if i == 15 {
            // else no space for length field, so will be in next chunk
            // set where length field would have been to 0's
            self.w[15] = 0;
        }
    }

    #[inline(always)]
    fn set_chunk_msg_len(&mut self, msg: &[u8]) {
        // the last 2 u32s are the length of the message in bits
        let msg_len = msg.len();
        let len = (msg_len * 8) as u64;
        let len_upper_bytes = ((len >> 32) as u32).to_be_bytes();
        let len_lower_bytes = ((len & 0xFFFFFFFF) as u32).to_be_bytes();
        self.w[14] = u32::from_be_bytes(len_upper_bytes);
        self.w[15] = u32::from_be_bytes(len_lower_bytes);
    }

    #[inline(always)]
    fn set_chunk_padding_zeros(&mut self, msg: &[u8], start: usize) {
        // the padding is all zeros except for the last 2 u32s which are the length of the message in bits
        for i in start..14 {
            self.w[i] = 0;
        }
    }

    #[inline(always)]
    fn set_chunk_padding_start_byte(&mut self) {
        // set a u32 to [0b10000000, 0, 0, 0]. The first by is 0b10000000, which is the flag to indicate the start of padding
        self.w[0] = 2147483648; // [0b10000000, 0, 0, 0] converted to u32
    }

    /// Processes a single chunk of the message using the SHA-256 algorithm.
    #[inline(always)]
    fn process_chunk(&mut self) {
        unsafe {
            // Extend w to 64 words
            // partially unrolled loop, 8 iterations at a time
            // why 8? gets a reasonable amount of variable reuse through the indexing of the w array, but doesn't unroll the loop too a point where the code size is too large for the gains
            for i in (16..64).step_by(8) {
                // could reuse repeats of variables, but we don't because benchmarks show it's slower. I _think_ it's something to do with cache hits for array elements being faster than reusing variables

                // First iteration: i
                let w15_0 = self.w[i - 15];
                let s0_0 = w15_0.rotate_right(7) ^ w15_0.rotate_right(18) ^ (w15_0 >> 3);
                let w2_0 = self.w[i - 2];
                let s1_0 = w2_0.rotate_right(17) ^ w2_0.rotate_right(19) ^ (w2_0 >> 10);
                self.w[i] = self.w[i - 16]
                    .wrapping_add(s0_0)
                    .wrapping_add(self.w[i - 7])
                    .wrapping_add(s1_0);

                // Second iteration: i + 1
                let w15_1 = self.w[i - 14];
                let s0_1 = w15_1.rotate_right(7) ^ w15_1.rotate_right(18) ^ (w15_1 >> 3);
                let w2_1 = self.w[i - 1];
                let s1_1 = w2_1.rotate_right(17) ^ w2_1.rotate_right(19) ^ (w2_1 >> 10);
                self.w[i + 1] = self.w[i - 15]
                    .wrapping_add(s0_1)
                    .wrapping_add(self.w[i - 6])
                    .wrapping_add(s1_1);

                // Third iteration: i + 2
                let w15_2 = self.w[i - 13];
                let s0_2 = w15_2.rotate_right(7) ^ w15_2.rotate_right(18) ^ (w15_2 >> 3);
                let w2_2 = self.w[i];
                let s1_2 = w2_2.rotate_right(17) ^ w2_2.rotate_right(19) ^ (w2_2 >> 10);
                self.w[i + 2] = self.w[i - 14]
                    .wrapping_add(s0_2)
                    .wrapping_add(self.w[i - 5])
                    .wrapping_add(s1_2);

                // Fourth iteration: i + 3
                let w15_3 = self.w[i - 12];
                let s0_3 = w15_3.rotate_right(7) ^ w15_3.rotate_right(18) ^ (w15_3 >> 3);
                let w2_3 = self.w[i + 1];
                let s1_3 = w2_3.rotate_right(17) ^ w2_3.rotate_right(19) ^ (w2_3 >> 10);
                self.w[i + 3] = self.w[i - 13]
                    .wrapping_add(s0_3)
                    .wrapping_add(self.w[i - 4])
                    .wrapping_add(s1_3);

                // Fifth iteration: i + 4
                let w15_4 = self.w[i - 11];
                let s0_4 = w15_4.rotate_right(7) ^ w15_4.rotate_right(18) ^ (w15_4 >> 3);
                let w2_4 = self.w[i + 2];
                let s1_4 = w2_4.rotate_right(17) ^ w2_4.rotate_right(19) ^ (w2_4 >> 10);
                self.w[i + 4] = self.w[i - 12]
                    .wrapping_add(s0_4)
                    .wrapping_add(self.w[i - 3])
                    .wrapping_add(s1_4);

                // Sixth iteration: i + 5
                let w15_5 = self.w[i - 10];
                let s0_5 = w15_5.rotate_right(7) ^ w15_5.rotate_right(18) ^ (w15_5 >> 3);
                let w2_5 = self.w[i + 3];
                let s1_5 = w2_5.rotate_right(17) ^ w2_5.rotate_right(19) ^ (w2_5 >> 10);
                self.w[i + 5] = self.w[i - 11]
                    .wrapping_add(s0_5)
                    .wrapping_add(self.w[i - 2])
                    .wrapping_add(s1_5);

                // Seventh iteration: i + 6
                let w15_6 = self.w[i - 9];
                let s0_6 = w15_6.rotate_right(7) ^ w15_6.rotate_right(18) ^ (w15_6 >> 3);
                let w2_6 = self.w[i + 4];
                let s1_6 = w2_6.rotate_right(17) ^ w2_6.rotate_right(19) ^ (w2_6 >> 10);
                self.w[i + 6] = self.w[i - 10]
                    .wrapping_add(s0_6)
                    .wrapping_add(self.w[i - 1])
                    .wrapping_add(s1_6);

                // Eighth iteration: i + 7
                let w15_7 = self.w[i - 8];
                let s0_7 = w15_7.rotate_right(7) ^ w15_7.rotate_right(18) ^ (w15_7 >> 3);
                let w2_7 = self.w[i + 5];
                let s1_7 = w2_7.rotate_right(17) ^ w2_7.rotate_right(19) ^ (w2_7 >> 10);
                self.w[i + 7] = self.w[i - 9]
                    .wrapping_add(s0_7)
                    .wrapping_add(self.w[i])
                    .wrapping_add(s1_7);
            }

            let mut a = self.h0;
            let mut b = self.h1;
            let mut c = self.h2;
            let mut d = self.h3;
            let mut e = self.h4;
            let mut f = self.h5;
            let mut g = self.h6;
            let mut h = self.h7;

            // partially unrolled loop, 8 iterations at a time
            for i in (0..64).step_by(8) {
                // First iteration: i
                let s1_0 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_0 = (e & f) ^ ((!e) & g);
                let temp1_0 = h
                    .wrapping_add(s1_0)
                    .wrapping_add(ch_0)
                    .wrapping_add(K[i])
                    .wrapping_add(self.w[i]);
                let s0_0 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_0 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_0 = s0_0.wrapping_add(maj_0);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_0);
                d = c;
                c = b;
                b = a;
                a = temp1_0.wrapping_add(temp2_0);

                // Second iteration: i + 1
                let s1_1 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_1 = (e & f) ^ ((!e) & g);
                let temp1_1 = h
                    .wrapping_add(s1_1)
                    .wrapping_add(ch_1)
                    .wrapping_add(K[i + 1])
                    .wrapping_add(self.w[i + 1]);
                let s0_1 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_1 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_1 = s0_1.wrapping_add(maj_1);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_1);
                d = c;
                c = b;
                b = a;
                a = temp1_1.wrapping_add(temp2_1);

                // Third iteration: i + 2
                let s1_2 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_2 = (e & f) ^ ((!e) & g);
                let temp1_2 = h
                    .wrapping_add(s1_2)
                    .wrapping_add(ch_2)
                    .wrapping_add(K[i + 2])
                    .wrapping_add(self.w[i + 2]);
                let s0_2 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_2 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_2 = s0_2.wrapping_add(maj_2);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_2);
                d = c;
                c = b;
                b = a;
                a = temp1_2.wrapping_add(temp2_2);

                // Fourth iteration: i + 3
                let s1_3 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_3 = (e & f) ^ ((!e) & g);
                let temp1_3 = h
                    .wrapping_add(s1_3)
                    .wrapping_add(ch_3)
                    .wrapping_add(K[i + 3])
                    .wrapping_add(self.w[i + 3]);
                let s0_3 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_3 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_3 = s0_3.wrapping_add(maj_3);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_3);
                d = c;
                c = b;
                b = a;
                a = temp1_3.wrapping_add(temp2_3);

                // Fifth iteration: i + 4
                let s1_4 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_4 = (e & f) ^ ((!e) & g);
                let temp1_4 = h
                    .wrapping_add(s1_4)
                    .wrapping_add(ch_4)
                    .wrapping_add(K[i + 4])
                    .wrapping_add(self.w[i + 4]);
                let s0_4 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_4 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_4 = s0_4.wrapping_add(maj_4);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_4);
                d = c;
                c = b;
                b = a;
                a = temp1_4.wrapping_add(temp2_4);

                // Sixth iteration: i + 5
                let s1_5 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_5 = (e & f) ^ ((!e) & g);
                let temp1_5 = h
                    .wrapping_add(s1_5)
                    .wrapping_add(ch_5)
                    .wrapping_add(K[i + 5])
                    .wrapping_add(self.w[i + 5]);
                let s0_5 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_5 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_5 = s0_5.wrapping_add(maj_5);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_5);
                d = c;
                c = b;
                b = a;
                a = temp1_5.wrapping_add(temp2_5);

                // Seventh iteration: i + 6
                let s1_6 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_6 = (e & f) ^ ((!e) & g);
                let temp1_6 = h
                    .wrapping_add(s1_6)
                    .wrapping_add(ch_6)
                    .wrapping_add(K[i + 6])
                    .wrapping_add(self.w[i + 6]);
                let s0_6 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_6 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_6 = s0_6.wrapping_add(maj_6);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_6);
                d = c;
                c = b;
                b = a;
                a = temp1_6.wrapping_add(temp2_6);

                // Eighth iteration: i + 7
                let s1_7 = e.rotate_right(6) ^ e.rotate_right(11) ^ e.rotate_right(25);
                let ch_7 = (e & f) ^ ((!e) & g);
                let temp1_7 = h
                    .wrapping_add(s1_7)
                    .wrapping_add(ch_7)
                    .wrapping_add(K[i + 7])
                    .wrapping_add(self.w[i + 7]);
                let s0_7 = a.rotate_right(2) ^ a.rotate_right(13) ^ a.rotate_right(22);
                let maj_7 = (a & b) ^ (a & c) ^ (b & c);
                let temp2_7 = s0_7.wrapping_add(maj_7);

                h = g;
                g = f;
                f = e;
                e = d.wrapping_add(temp1_7);
                d = c;
                c = b;
                b = a;
                a = temp1_7.wrapping_add(temp2_7);
            }

            self.h0 = self.h0.wrapping_add(a);
            self.h1 = self.h1.wrapping_add(b);
            self.h2 = self.h2.wrapping_add(c);
            self.h3 = self.h3.wrapping_add(d);
            self.h4 = self.h4.wrapping_add(e);
            self.h5 = self.h5.wrapping_add(f);
            self.h6 = self.h6.wrapping_add(g);
            self.h7 = self.h7.wrapping_add(h);
        }
    }

    /// Computes the SHA-256 digest of the given message.
    ///
    /// # Arguments
    /// * `msg` - A byte slice representing the message to be hashed.
    ///
    /// # Returns
    /// A 32-byte array representing the SHA-256 hash of the message.
    pub fn digest(&mut self, msg: &[u8]) -> [u8; 32] {
        self.h0 = 0x6a09e667;
        self.h1 = 0xbb67ae85;
        self.h2 = 0x3c6ef372;
        self.h3 = 0xa54ff53a;
        self.h4 = 0x510e527f;
        self.h5 = 0x9b05688c;
        self.h6 = 0x1f83d9ab;
        self.h7 = 0x5be0cd19;

        let msg_len = msg.len();
        let n_chunks_saturated = msg_len / 64; // how many full chunks the message fits into
        // for each chunk (64 bytes) of the message
        for i in 0..n_chunks_saturated {
            self.set_chunk(msg, i);
            self.process_chunk();
        }

        let msg_rem_len = msg_len % 64; // how many bytes from the message do not fit into a full chunk
        // the remaining message length is 0-63 bytes
        // the padding is 9 bytes (1 for the 0b10000000 byte, 8 for the message length in bits)
        // therefore:
            // a message of 1-55 bytes will fit into the last chunk WITH padding
            // a message of 56-63 bytes will require the 0b10000000 byte to be in the last chunk as the message, but the message length need an extra chunk
            // a message of 0 bytes will also require the extra chunk, but the 0b10000000 byte will be in the same chunk as the message length


        if msg_rem_len == 0 {
            self.set_chunk_padding_start_byte();
            self.set_chunk_padding_zeros(msg, 1);
            self.set_chunk_msg_len(msg);
        } else {
            // copy the remaining message into the w array
            self.set_chunk_last(msg, n_chunks_saturated);
        }
        self.process_chunk();
        if msg_rem_len > 55 {
            // an extra chunk is required for the padding
            // padding is all zeros with the message length in bits at the end
            self.set_chunk_padding_zeros(msg, 0);
            self.set_chunk_msg_len(msg);
            self.process_chunk();
        }

        // Create the output hash
        let mut hash = [0; 32];
        unsafe {
            hash[0..4].copy_from_slice(&self.h0.to_be_bytes());
            hash[4..8].copy_from_slice(&self.h1.to_be_bytes());
            hash[8..12].copy_from_slice(&self.h2.to_be_bytes());
            hash[12..16].copy_from_slice(&self.h3.to_be_bytes());
            hash[16..20].copy_from_slice(&self.h4.to_be_bytes());
            hash[20..24].copy_from_slice(&self.h5.to_be_bytes());
            hash[24..28].copy_from_slice(&self.h6.to_be_bytes());
            hash[28..32].copy_from_slice(&self.h7.to_be_bytes());
        }

        hash
    }
}

const K: [u32; 64] = [
    0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
    0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
    0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
    0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
    0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
    0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
    0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
    0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2,
];

#[cfg(test)]
mod tests {
	use super::*;
    use sha2::{digest::generic_array::GenericArray, Digest, Sha256 as Theirs};

    struct Rng {
        state: u64,
    }

    impl Rng {
        fn new(seed: u64) -> Self {
            Self {
                state: if seed == 0 { 1 } else { seed },
            }
        }

        fn next(&mut self) -> u64 {
            self.state ^= self.state << 13;
            self.state ^= self.state >> 7;
            self.state ^= self.state << 17;
            self.state
        }
    }

    #[test]
    fn test_against_sha2_lib() {
        // generate random messages

        let mut rng = Rng::new(0);

        let limit = 100_000;
        let mut count: usize = 0;
        let mut ours = Sha256::new();
        loop {
            let mut theirs = sha2::Sha256::new();
            let mut message_bytes = Vec::<u8>::new();
            let i = rng.next() % 1024;
            for _ in 0..=i {
                message_bytes.push((rng.next() % 255) as u8); // 'a'
            }
            let hash = ours.digest(&message_bytes);
            theirs.update(&message_bytes);
            let hash2 = theirs.finalize();
            println!("our hash: {:?}", hash);
            println!("their hash: {:?}", hash2);
            assert_eq!(hash, hash2.as_slice(), "hashes[{}] with {}x'a'", i, i+1);
            
            count += 1;
            if count == limit {
                break;
            }
        }
        println!("total test cases: {}", count);
    }

    #[test]
    fn hash_hello() {
		let mut sha256 = Sha256::new();
		let message_bytes = &[104, 101, 108, 108, 111];
		let hash = sha256.digest(message_bytes);
		assert_eq!(hash, [
            44, 242, 77, 186,  95, 176, 163,  14,
            38, 232, 59,  42, 197, 185, 226, 158,
            27,  22, 30,  92,  31, 167,  66,  94,
           115,   4, 51,  98, 147, 139, 152,  36
         ]);
    }

    #[test]
    fn hash_empty() {
		let mut sha256 = Sha256::new();
		let message_bytes = &[];
		let hash = sha256.digest(message_bytes);
		assert_eq!(hash, [
            227, 176, 196, 66, 152, 252, 28, 20, 154, 251, 244, 200, 153, 111, 185, 36, 39, 174, 65, 228, 100, 155, 147, 76, 164, 149, 153, 27, 120, 82, 184, 85
         ]);
    }

    // the first 1024 hashes of strings of length 0-1024 bytes, where each byte is 'a'. E.g:
    // ''
    // 'a'
    // 'aa'
    // 'aaa'
    // ...
    const HASHES: [[u8; 32]; 1024] = [[202, 151, 129, 18, 202, 27, 189, 202, 250, 194, 49, 179, 154, 35, 220, 77, 167, 134, 239, 248, 20, 124, 78, 114, 185, 128, 119, 133, 175, 238, 72, 187],
    [150, 27, 109, 211, 237, 227, 203, 142, 203, 170, 203, 214, 141, 224, 64, 205, 120, 235, 46, 213, 136, 145, 48, 204, 235, 76, 73, 38, 142, 164, 213, 6],
    [152, 52, 135, 109, 207, 176, 92, 177, 103, 165, 194, 73, 83, 235, 165, 140, 74, 200, 155, 26, 223, 87, 242, 143, 47, 157, 9, 175, 16, 126, 232, 240],
    [97, 190, 85, 168, 226, 246, 180, 225, 114, 51, 139, 221, 241, 132, 214, 219, 238, 41, 201, 136, 83, 224, 160, 72, 94, 206, 231, 242, 123, 154, 240, 180],
    [237, 150, 142, 132, 13, 16, 210, 211, 19, 168, 112, 188, 19, 26, 78, 44, 49, 29, 122, 208, 155, 223, 50, 179, 65, 129, 71, 34, 31, 81, 166, 226],
    [237, 2, 69, 123, 92, 65, 217, 100, 219, 210, 242, 166, 9, 214, 63, 225, 187, 117, 40, 219, 229, 94, 26, 191, 91, 82, 194, 73, 205, 115, 87, 151],
    [228, 98, 64, 113, 75, 93, 179, 162, 62, 238, 96, 71, 154, 98, 62, 251, 164, 214, 51, 210, 127, 228, 240, 60, 144, 75, 158, 33, 154, 127, 190, 96],
    [31, 60, 228, 4, 21, 162, 8, 31, 163, 238, 231, 95, 195, 159, 255, 142, 86, 194, 34, 112, 209, 169, 120, 167, 36, 155, 89, 45, 206, 189, 32, 180],
    [242, 172, 169, 59, 128, 202, 230, 129, 34, 31, 4, 69, 250, 78, 44, 174, 138, 31, 159, 143, 161, 225, 116, 29, 150, 57, 202, 173, 34, 47, 83, 125],
    [191, 44, 181, 138, 104, 246, 132, 217, 90, 59, 120, 239, 143, 102, 28, 154, 78, 91, 9, 232, 44, 200, 249, 204, 136, 204, 233, 5, 40, 202, 235, 39],
    [40, 203, 1, 125, 252, 153, 7, 58, 161, 180, 124, 27, 48, 244, 19, 227, 206, 119, 76, 73, 145, 235, 65, 88, 222, 80, 249, 219, 179, 109, 128, 67],
    [242, 74, 188, 52, 177, 63, 173, 231, 110, 128, 87, 153, 247, 17, 135, 218, 108, 217, 11, 156, 172, 55, 58, 230, 94, 213, 127, 20, 59, 214, 100, 229],
    [166, 137, 215, 134, 232, 19, 64, 228, 85, 17, 222, 198, 199, 171, 45, 151, 132, 52, 229, 219, 18, 51, 98, 69, 15, 225, 12, 250, 199, 13, 25, 208],
    [130, 202, 183, 223, 10, 191, 185, 217, 93, 202, 78, 89, 55, 206, 41, 104, 199, 152, 199, 38, 254, 164, 140, 1, 107, 249, 118, 50, 33, 239, 218, 19],
    [239, 45, 240, 181, 57, 198, 194, 61, 224, 244, 203, 228, 38, 72, 195, 1, 174, 14, 34, 232, 135, 52, 10, 69, 153, 251, 78, 244, 226, 103, 142, 72],
    [12, 11, 234, 206, 248, 135, 123, 191, 36, 22, 235, 0, 242, 181, 220, 150, 53, 78, 38, 221, 29, 245, 81, 115, 32, 69, 155, 18, 54, 134, 15, 140],
    [184, 96, 102, 110, 226, 150, 109, 216, 249, 3, 190, 68, 238, 96, 92, 110, 19, 102, 249, 38, 217, 241, 122, 143, 73, 147, 125, 17, 98, 78, 185, 157],
    [201, 38, 222, 250, 170, 61, 19, 237, 162, 252, 99, 165, 83, 187, 127, 183, 50, 107, 236, 230, 231, 203, 103, 202, 82, 150, 228, 114, 125, 137, 186, 180],
    [160, 180, 170, 171, 138, 150, 110, 33, 147, 186, 23, 45, 104, 22, 44, 70, 86, 134, 1, 151, 242, 86, 181, 244, 95, 2, 3, 57, 127, 243, 249, 156],
    [66, 73, 45, 160, 98, 52, 173, 10, 199, 111, 93, 93, 235, 219, 109, 26, 224, 39, 207, 251, 231, 70, 161, 193, 59, 137, 187, 139, 192, 19, 145, 55],
    [125, 248, 226, 153, 200, 52, 222, 25, 142, 38, 76, 62, 55, 75, 197, 142, 205, 147, 130, 37, 42, 112, 92, 24, 59, 235, 2, 242, 117, 87, 30, 59],
    [236, 124, 73, 77, 246, 210, 167, 234, 54, 102, 141, 101, 110, 107, 137, 121, 227, 54, 65, 191, 234, 55, 140, 21, 3, 138, 243, 150, 77, 176, 87, 163],
    [137, 125, 62, 149, 182, 95, 38, 103, 96, 129, 248, 185, 243, 169, 139, 110, 228, 66, 69, 102, 48, 62, 141, 78, 124, 117, 34, 235, 174, 33, 158, 171],
    [9, 246, 31, 141, 156, 214, 94, 106, 12, 37, 128, 135, 196, 133, 182, 41, 53, 65, 54, 78, 66, 189, 151, 178, 215, 147, 101, 128, 200, 170, 60, 84],
    [47, 82, 30, 42, 125, 11, 216, 18, 203, 192, 53, 244, 237, 104, 6, 235, 141, 133, 23, 147, 176, 75, 161, 71, 232, 246, 107, 114, 245, 209, 242, 15],
    [153, 118, 213, 73, 162, 81, 21, 218, 180, 227, 109, 12, 31, 184, 243, 28, 176, 125, 168, 125, 216, 50, 117, 151, 115, 96, 235, 125, 192, 158, 136, 222],
    [204, 6, 22, 230, 28, 189, 110, 142, 94, 52, 233, 251, 45, 50, 15, 55, 222, 145, 88, 32, 32, 111, 86, 150, 195, 31, 31, 189, 36, 170, 22, 222],
    [156, 84, 124, 184, 17, 90, 68, 136, 59, 159, 112, 186, 104, 247, 81, 23, 205, 85, 53, 156, 146, 97, 24, 117, 227, 134, 248, 175, 152, 193, 114, 171],
    [105, 19, 201, 199, 253, 66, 254, 35, 223, 139, 107, 205, 77, 186, 241, 193, 119, 72, 148, 141, 151, 242, 152, 11, 67, 35, 25, 195, 158, 221, 207, 108],
    [58, 84, 252, 12, 188, 11, 14, 244, 139, 101, 7, 183, 120, 128, 150, 35, 93, 16, 41, 45, 211, 174, 36, 226, 47, 90, 160, 98, 212, 249, 134, 74],
    [97, 198, 11, 72, 125, 26, 146, 30, 11, 204, 155, 248, 83, 221, 160, 251, 21, 155, 48, 191, 87, 178, 226, 210, 199, 83, 176, 11, 225, 91, 90, 9],
    [59, 163, 245, 244, 59, 146, 96, 38, 131, 193, 154, 238, 98, 162, 3, 66, 176, 132, 221, 89, 113, 221, 211, 56, 8, 216, 26, 50, 136, 121, 165, 71],
    [133, 39, 133, 200, 5, 199, 126, 113, 162, 35, 64, 165, 78, 157, 149, 147, 62, 212, 145, 33, 231, 210, 191, 60, 45, 53, 136, 84, 188, 19, 89, 234],
    [162, 124, 137, 108, 72, 89, 32, 72, 67, 22, 106, 246, 111, 14, 144, 43, 156, 59, 62, 214, 210, 253, 19, 212, 53, 171, 192, 32, 6, 92, 82, 111],
    [98, 147, 98, 175, 198, 44, 116, 73, 124, 174, 210, 39, 46, 48, 248, 18, 94, 205, 9, 101, 248, 216, 215, 207, 196, 226, 96, 247, 248, 221, 49, 157],
    [34, 193, 210, 75, 205, 3, 233, 174, 233, 131, 46, 252, 205, 109, 166, 19, 252, 112, 39, 147, 23, 142, 95, 18, 201, 69, 199, 182, 125, 221, 169, 51],
    [33, 236, 5, 91, 56, 206, 117, 156, 212, 208, 244, 119, 233, 189, 236, 44, 91, 129, 153, 148, 93, 180, 67, 155, 174, 51, 74, 150, 77, 246, 36, 108],
    [54, 90, 156, 62, 44, 42, 240, 165, 110, 71, 169, 218, 197, 28, 44, 83, 129, 191, 143, 65, 39, 59, 173, 49, 117, 224, 230, 25, 18, 106, 208, 135],
    [180, 213, 229, 110, 146, 155, 164, 205, 163, 73, 233, 39, 78, 54, 3, 208, 190, 36, 107, 130, 1, 107, 202, 32, 243, 99, 150, 60, 95, 45, 104, 69],
    [227, 60, 223, 156, 127, 113, 32, 185, 142, 140, 120, 64, 137, 83, 224, 127, 46, 205, 24, 48, 6, 181, 96, 109, 243, 73, 180, 194, 18, 172, 244, 62],
    [192, 248, 189, 77, 188, 43, 12, 3, 16, 124, 28, 55, 145, 63, 42, 117, 1, 245, 33, 70, 127, 69, 221, 15, 239, 105, 88, 233, 164, 105, 39, 25],
    [122, 83, 134, 7, 253, 170, 185, 41, 105, 149, 146, 159, 69, 21, 101, 187, 184, 20, 46, 24, 68, 17, 115, 34, 170, 253, 43, 61, 118, 176, 26, 255],
    [102, 211, 79, 186, 113, 248, 244, 80, 247, 228, 85, 152, 133, 62, 83, 191, 194, 59, 189, 18, 144, 39, 203, 177, 49, 162, 244, 255, 215, 135, 140, 208],
    [22, 132, 152, 119, 198, 194, 30, 240, 191, 166, 142, 79, 103, 71, 48, 13, 219, 23, 27, 23, 11, 159, 0, 225, 137, 237, 196, 194, 252, 77, 185, 62],
    [82, 120, 158, 52, 35, 183, 43, 238, 184, 152, 69, 106, 79, 73, 102, 46, 70, 176, 203, 185, 96, 120, 76, 94, 244, 177, 57, 157, 50, 126, 124, 39],
    [102, 67, 17, 12, 86, 40, 255, 245, 158, 223, 118, 216, 45, 91, 245, 115, 191, 128, 15, 22, 164, 214, 93, 251, 30, 93, 111, 26, 70, 41, 109, 11],
    [17, 234, 237, 147, 44, 108, 111, 221, 252, 46, 252, 57, 78, 96, 159, 172, 244, 171, 232, 20, 252, 97, 128, 208, 59, 20, 252, 225, 58, 7, 208, 229],
    [151, 218, 172, 14, 233, 153, 141, 252, 173, 108, 156, 9, 112, 218, 92, 164, 17, 200, 98, 51, 169, 68, 194, 91, 71, 86, 111, 106, 123, 193, 221, 213],
    [143, 155, 236, 106, 98, 221, 40, 235, 211, 109, 18, 39, 116, 85, 146, 222, 102, 88, 179, 105, 116, 163, 187, 152, 164, 197, 130, 246, 131, 234, 108, 66],
    [22, 11, 78, 67, 62, 56, 78, 5, 229, 55, 220, 89, 180, 103, 247, 203, 36, 3, 240, 33, 77, 177, 92, 93, 181, 136, 98, 163, 241, 21, 109, 46],
    [191, 197, 254, 14, 54, 1, 82, 202, 152, 197, 15, 171, 78, 215, 227, 7, 140, 23, 222, 188, 41, 23, 116, 13, 80, 0, 145, 59, 104, 108, 161, 41],
    [108, 27, 61, 199, 167, 6, 185, 220, 129, 53, 42, 103, 22, 185, 198, 102, 198, 8, 216, 98, 98, 114, 198, 75, 145, 74, 176, 85, 114, 252, 110, 132],
    [171, 227, 70, 167, 37, 159, 201, 11, 76, 39, 24, 84, 25, 98, 142, 94, 106, 246, 70, 107, 26, 233, 181, 68, 108, 172, 75, 252, 38, 207, 5, 196],
    [163, 240, 27, 105, 57, 37, 97, 39, 88, 42, 200, 174, 159, 180, 122, 56, 42, 36, 70, 128, 128, 106, 63, 97, 58, 17, 136, 81, 193, 202, 29, 71],
    [159, 67, 144, 248, 211, 12, 45, 217, 46, 201, 240, 149, 182, 94, 43, 154, 233, 176, 169, 37, 165, 37, 142, 36, 28, 159, 30, 145, 15, 115, 67, 24],
    [179, 84, 57, 164, 172, 111, 9, 72, 182, 214, 249, 227, 198, 175, 15, 95, 89, 12, 226, 15, 27, 222, 112, 144, 239, 121, 112, 104, 110, 198, 115, 138],
    [241, 59, 45, 114, 70, 89, 235, 59, 244, 127, 45, 214, 175, 26, 204, 200, 123, 129, 240, 159, 89, 242, 183, 94, 92, 11, 237, 101, 137, 223, 232, 198],
    [213, 192, 57, 183, 72, 170, 100, 102, 87, 130, 151, 78, 195, 220, 48, 37, 192, 66, 237, 245, 77, 205, 194, 181, 222, 49, 56, 91, 9, 76, 182, 120],
    [17, 27, 178, 97, 39, 122, 253, 101, 240, 116, 75, 36, 124, 211, 228, 125, 56, 109, 113, 86, 61, 14, 217, 149, 81, 120, 7, 213, 235, 212, 251, 163],
    [17, 238, 57, 18, 17, 198, 37, 100, 96, 182, 237, 55, 89, 87, 250, 221, 128, 97, 202, 251, 179, 29, 175, 150, 125, 184, 117, 174, 189, 90, 170, 212],
    [53, 213, 252, 23, 207, 187, 173, 208, 15, 94, 113, 10, 218, 57, 241, 148, 197, 173, 124, 118, 106, 214, 112, 114, 36, 95, 31, 173, 69, 240, 245, 48],
    [245, 6, 137, 140, 199, 194, 224, 146, 249, 235, 159, 173, 174, 123, 165, 3, 131, 245, 180, 106, 42, 79, 229, 89, 125, 187, 85, 58, 120, 152, 18, 104],
    [125, 62, 116, 160, 93, 125, 177, 91, 206, 74, 217, 236, 6, 88, 234, 152, 227, 240, 110, 238, 207, 22, 180, 198, 255, 242, 218, 69, 125, 220, 47, 52],
    [255, 224, 84, 254, 122, 224, 203, 109, 198, 92, 58, 249, 182, 29, 82, 9, 244, 57, 133, 29, 180, 61, 11, 165, 153, 115, 55, 223, 21, 70, 104, 235],
    [99, 83, 97, 196, 139, 185, 234, 177, 65, 152, 231, 110, 168, 171, 127, 26, 65, 104, 93, 106, 214, 42, 169, 20, 109, 48, 29, 79, 23, 235, 10, 224],
    [172, 19, 127, 206, 73, 131, 124, 124, 41, 69, 246, 22, 13, 60, 14, 103, 158, 111, 64, 7, 8, 80, 66, 10, 34, 188, 16, 224, 105, 44, 189, 199],
    [97, 22, 192, 159, 137, 113, 142, 130, 159, 105, 183, 175, 177, 217, 214, 12, 105, 115, 147, 93, 150, 179, 50, 19, 228, 210, 134, 137, 254, 16, 142, 231],
    [87, 76, 97, 229, 242, 170, 211, 110, 197, 40, 236, 244, 198, 222, 68, 121, 63, 157, 171, 6, 179, 141, 28, 90, 65, 248, 169, 214, 75, 78, 213, 59],
    [239, 94, 212, 110, 237, 32, 2, 25, 23, 36, 219, 87, 179, 52, 69, 120, 137, 201, 173, 79, 62, 112, 39, 205, 215, 221, 65, 52, 13, 183, 93, 17],
    [107, 213, 229, 3, 72, 85, 161, 18, 65, 240, 222, 232, 252, 114, 133, 15, 253, 153, 85, 178, 131, 71, 168, 100, 40, 181, 250, 25, 17, 159, 106, 208],
    [238, 250, 76, 251, 234, 121, 64, 12, 47, 66, 57, 225, 247, 2, 224, 46, 190, 206, 118, 31, 120, 182, 163, 92, 157, 44, 22, 122, 121, 249, 87, 12],
    [214, 99, 4, 182, 24, 3, 101, 228, 124, 133, 143, 108, 132, 211, 218, 6, 92, 175, 75, 51, 80, 201, 244, 82, 119, 161, 175, 130, 227, 219, 176, 85],
    [14, 5, 142, 63, 125, 4, 57, 249, 5, 77, 89, 199, 53, 88, 122, 233, 150, 85, 246, 71, 58, 35, 76, 228, 148, 216, 43, 85, 134, 247, 234, 198],
    [246, 56, 53, 157, 13, 184, 96, 207, 48, 203, 94, 103, 68, 152, 105, 56, 199, 1, 83, 4, 62, 254, 138, 52, 131, 84, 178, 117, 216, 126, 206, 116],
    [138, 248, 129, 188, 136, 137, 91, 217, 216, 206, 169, 117, 167, 208, 109, 192, 39, 93, 157, 185, 213, 127, 19, 130, 22, 147, 107, 101, 232, 176, 100, 137],
    [248, 184, 171, 166, 82, 229, 179, 205, 230, 188, 116, 188, 183, 191, 241, 82, 137, 162, 34, 207, 219, 119, 89, 169, 128, 157, 192, 133, 116, 145, 31, 96],
    [188, 25, 185, 211, 85, 65, 26, 78, 61, 52, 38, 245, 211, 155, 252, 154, 133, 108, 165, 240, 66, 188, 58, 70, 133, 114, 8, 0, 134, 173, 19, 132],
    [211, 71, 113, 113, 214, 248, 10, 2, 182, 65, 85, 56, 253, 213, 130, 20, 73, 16, 201, 184, 72, 43, 152, 42, 27, 98, 180, 65, 242, 29, 200, 25],
    [218, 167, 107, 77, 22, 103, 153, 87, 131, 50, 38, 168, 132, 69, 6, 9, 138, 55, 186, 201, 73, 121, 241, 203, 252, 108, 74, 195, 176, 155, 155, 96],
    [15, 69, 232, 88, 251, 196, 23, 108, 223, 78, 65, 31, 136, 40, 30, 222, 252, 57, 10, 229, 175, 231, 223, 15, 68, 205, 146, 151, 240, 166, 69, 128],
    [140, 72, 40, 13, 87, 251, 136, 241, 97, 173, 243, 77, 159, 89, 125, 147, 202, 50, 183, 237, 252, 210, 59, 42, 254, 100, 195, 120, 155, 63, 120, 85],
    [245, 133, 67, 89, 129, 156, 220, 244, 78, 23, 231, 110, 184, 0, 206, 55, 215, 115, 62, 187, 145, 147, 117, 97, 149, 115, 31, 33, 150, 77, 49, 161],
    [225, 78, 255, 51, 16, 186, 187, 125, 99, 147, 62, 129, 57, 131, 59, 95, 47, 10, 62, 200, 10, 11, 208, 30, 222, 222, 151, 243, 193, 237, 213, 43],
    [245, 71, 80, 34, 254, 182, 152, 112, 41, 91, 156, 30, 120, 197, 164, 145, 147, 116, 6, 29, 83, 69, 22, 120, 21, 128, 24, 121, 249, 49, 235, 176],
    [132, 46, 245, 48, 182, 221, 140, 81, 23, 111, 217, 93, 153, 69, 223, 58, 117, 101, 6, 170, 140, 74, 53, 250, 104, 187, 94, 31, 161, 74, 202, 100],
    [205, 222, 76, 38, 254, 189, 249, 210, 243, 179, 74, 29, 234, 149, 187, 210, 40, 11, 242, 32, 127, 100, 161, 180, 4, 96, 142, 49, 163, 196, 177, 151],
    [207, 185, 36, 197, 45, 156, 61, 245, 168, 83, 196, 27, 87, 255, 137, 65, 245, 110, 117, 224, 99, 99, 80, 186, 75, 53, 144, 251, 20, 230, 196, 45],
    [151, 83, 141, 134, 97, 232, 215, 92, 143, 197, 159, 122, 117, 155, 27, 174, 179, 203, 246, 202, 40, 43, 144, 1, 111, 167, 108, 192, 90, 54, 230, 216],
    [94, 75, 84, 95, 165, 226, 252, 53, 66, 43, 196, 36, 78, 241, 136, 116, 90, 184, 11, 83, 36, 54, 207, 138, 106, 28, 68, 85, 26, 35, 91, 216],
    [107, 46, 199, 145, 112, 245, 14, 165, 123, 136, 109, 200, 26, 44, 247, 135, 33, 198, 81, 160, 2, 200, 54, 90, 82, 64, 25, 167, 237, 90, 138, 64],
    [155, 159, 231, 240, 164, 140, 43, 154, 235, 112, 250, 8, 40, 193, 7, 128, 161, 89, 126, 24, 246, 113, 235, 40, 78, 15, 178, 225, 28, 154, 123, 168],
    [187, 136, 36, 57, 1, 59, 251, 9, 60, 88, 187, 233, 74, 33, 218, 106, 4, 165, 16, 218, 154, 108, 150, 151, 187, 74, 232, 221, 103, 65, 138, 43],
    [150, 231, 139, 90, 131, 222, 153, 95, 143, 160, 2, 252, 164, 241, 130, 216, 191, 232, 202, 149, 89, 118, 251, 178, 141, 57, 220, 189, 148, 190, 20, 147],
    [133, 9, 74, 56, 101, 26, 7, 2, 7, 115, 100, 131, 173, 161, 125, 152, 41, 138, 128, 18, 92, 0, 92, 116, 213, 137, 151, 191, 93, 42, 198, 144],
    [225, 200, 68, 131, 209, 216, 136, 119, 128, 33, 136, 69, 188, 191, 108, 238, 75, 40, 55, 58, 43, 189, 22, 149, 231, 211, 226, 210, 74, 246, 48, 151],
    [238, 76, 170, 85, 24, 168, 102, 243, 62, 23, 77, 110, 113, 186, 57, 97, 168, 108, 160, 10, 116, 134, 177, 50, 229, 169, 240, 27, 250, 161, 215, 148],
    [42, 44, 96, 254, 150, 175, 172, 145, 81, 212, 189, 147, 47, 219, 69, 190, 44, 126, 23, 94, 2, 176, 89, 132, 38, 202, 193, 92, 56, 81, 28, 180],
    [151, 13, 49, 180, 40, 222, 143, 234, 116, 177, 100, 132, 216, 168, 173, 178, 201, 225, 189, 151, 77, 124, 98, 31, 208, 67, 50, 188, 52, 153, 241, 23],
    [19, 40, 68, 104, 29, 87, 213, 174, 118, 223, 211, 90, 7, 228, 252, 16, 253, 192, 206, 159, 8, 130, 162, 176, 201, 219, 14, 132, 17, 109, 91, 173],
    [40, 22, 89, 120, 136, 228, 160, 211, 163, 107, 130, 184, 51, 22, 171, 50, 104, 14, 184, 240, 15, 140, 211, 185, 4, 214, 129, 36, 109, 40, 90, 14],
    [157, 7, 147, 57, 121, 145, 181, 122, 153, 160, 124, 110, 107, 74, 146, 186, 182, 141, 191, 96, 83, 69, 205, 11, 135, 243, 133, 164, 72, 167, 38, 188],
    [242, 24, 55, 17, 207, 252, 221, 32, 185, 155, 113, 253, 167, 116, 85, 246, 11, 149, 124, 253, 34, 71, 157, 42, 133, 184, 125, 88, 90, 91, 131, 5],
    [225, 213, 109, 197, 180, 161, 164, 244, 126, 23, 166, 228, 41, 221, 198, 173, 186, 113, 37, 107, 164, 129, 93, 243, 233, 122, 212, 175, 13, 251, 77, 177],
    [65, 229, 201, 32, 193, 33, 20, 88, 139, 142, 92, 205, 242, 109, 137, 26, 105, 103, 254, 254, 183, 126, 27, 26, 47, 75, 127, 181, 146, 82, 22, 198],
    [99, 21, 74, 76, 130, 185, 156, 123, 9, 192, 16, 217, 113, 56, 236, 234, 91, 162, 199, 225, 118, 232, 180, 104, 87, 206, 67, 120, 182, 242, 88, 116],
    [93, 92, 143, 182, 182, 20, 147, 36, 142, 24, 67, 239, 143, 185, 135, 95, 242, 139, 146, 7, 94, 110, 184, 126, 21, 60, 175, 70, 152, 189, 172, 195],
    [62, 36, 83, 28, 218, 165, 149, 171, 86, 249, 118, 185, 108, 26, 29, 248, 0, 158, 171, 236, 48, 10, 90, 2, 97, 192, 228, 79, 71, 164, 59, 137],
    [12, 239, 13, 168, 28, 139, 121, 207, 177, 63, 149, 195, 121, 165, 182, 57, 38, 98, 227, 98, 61, 222, 91, 204, 91, 243, 58, 1, 17, 53, 108, 14],
    [56, 159, 41, 242, 223, 169, 64, 158, 233, 23, 110, 198, 86, 93, 138, 150, 131, 149, 22, 177, 105, 115, 70, 31, 25, 247, 185, 216, 199, 58, 130, 37],
    [145, 200, 116, 146, 196, 43, 166, 212, 1, 9, 158, 13, 124, 144, 147, 4, 227, 22, 81, 13, 254, 75, 110, 26, 128, 27, 204, 72, 150, 62, 97, 203],
    [99, 116, 247, 50, 8, 133, 68, 115, 130, 127, 111, 106, 63, 67, 177, 245, 62, 170, 59, 130, 194, 28, 26, 109, 105, 162, 17, 11, 42, 121, 186, 173],
    [245, 67, 83, 0, 138, 37, 83, 38, 46, 205, 196, 163, 71, 73, 86, 59, 160, 149, 14, 139, 15, 200, 101, 39, 128, 176, 166, 20, 185, 150, 131, 193],
    [186, 2, 115, 26, 230, 149, 170, 229, 205, 73, 180, 157, 132, 51, 11, 99, 153, 87, 51, 235, 34, 16, 42, 202, 117, 95, 1, 121, 177, 224, 226, 15],
    [108, 183, 80, 178, 24, 22, 6, 81, 31, 74, 126, 71, 134, 181, 54, 146, 245, 26, 156, 220, 77, 49, 114, 253, 207, 185, 38, 122, 236, 167, 228, 228],
    [100, 65, 14, 101, 27, 52, 101, 36, 207, 229, 110, 104, 194, 55, 234, 118, 192, 55, 121, 33, 105, 112, 39, 235, 121, 74, 6, 117, 1, 251, 41, 16],
    [156, 170, 168, 51, 201, 50, 115, 249, 39, 180, 20, 95, 134, 164, 23, 145, 234, 110, 57, 163, 29, 17, 138, 106, 174, 61, 188, 218, 172, 95, 132, 172],
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    [55, 91, 127, 143, 0, 172, 237, 119, 100, 24, 120, 219, 237, 180, 9, 223, 81, 49, 118, 90, 202, 26, 181, 21, 82, 253, 155, 243, 236, 77, 102, 191],
    [23, 100, 53, 191, 144, 128, 17, 210, 81, 100, 252, 90, 14, 154, 148, 153, 233, 51, 170, 91, 217, 121, 31, 68, 68, 97, 42, 38, 3, 24, 100, 100],
    [222, 42, 226, 176, 227, 98, 119, 221, 119, 133, 66, 135, 240, 133, 41, 252, 61, 209, 204, 13, 139, 170, 247, 226, 215, 119, 6, 41, 32, 6, 178, 106],
    [4, 9, 16, 103, 186, 202, 190, 11, 67, 78, 231, 244, 48, 159, 112, 242, 147, 4, 153, 250, 13, 137, 159, 145, 46, 58, 204, 251, 141, 43, 82, 219],
    [0, 131, 76, 8, 94, 29, 204, 133, 98, 90, 168, 159, 13, 113, 134, 117, 217, 14, 209, 204, 116, 141, 239, 251, 113, 105, 176, 253, 46, 101, 140, 122],
    [232, 6, 120, 223, 173, 176, 112, 78, 94, 104, 74, 218, 11, 11, 231, 172, 47, 34, 84, 127, 19, 4, 254, 154, 180, 170, 167, 48, 217, 144, 154, 58],
    [75, 100, 43, 206, 60, 145, 171, 170, 137, 226, 137, 170, 65, 187, 204, 138, 128, 136, 177, 34, 159, 165, 175, 11, 122, 95, 28, 90, 118, 197, 136, 202],
    [111, 154, 219, 47, 189, 231, 59, 32, 66, 237, 127, 145, 124, 236, 138, 243, 180, 144, 154, 119, 154, 3, 104, 46, 160, 192, 173, 13, 241, 7, 105, 213],
    [202, 225, 5, 197, 204, 87, 219, 88, 241, 183, 134, 184, 101, 71, 67, 204, 250, 80, 215, 90, 127, 60, 248, 152, 135, 125, 145, 56, 76, 156, 183, 8],
    [144, 76, 248, 96, 236, 79, 150, 87, 201, 93, 200, 101, 166, 87, 119, 186, 134, 119, 123, 246, 134, 116, 140, 233, 122, 226, 80, 221, 69, 218, 94, 149],
    [55, 68, 87, 133, 5, 75, 222, 187, 60, 109, 195, 35, 225, 220, 252, 160, 223, 123, 37, 72, 221, 123, 145, 44, 71, 172, 5, 111, 176, 150, 37, 170],
    [201, 67, 132, 115, 145, 18, 46, 186, 156, 129, 156, 131, 161, 200, 229, 85, 179, 224, 229, 250, 175, 80, 81, 106, 225, 103, 17, 52, 111, 178, 218, 205],
    [238, 172, 28, 211, 117, 83, 191, 134, 45, 190, 171, 174, 52, 199, 94, 125, 135, 203, 198, 236, 104, 71, 192, 219, 236, 137, 59, 76, 248, 92, 250, 91],
    [179, 37, 129, 134, 82, 2, 52, 202, 238, 161, 12, 122, 208, 56, 53, 47, 104, 172, 105, 229, 71, 24, 22, 32, 206, 232, 225, 75, 41, 74, 180, 6],
    [6, 159, 227, 110, 199, 110, 49, 137, 72, 83, 212, 37, 177, 187, 196, 195, 189, 127, 103, 185, 183, 222, 67, 122, 168, 176, 238, 192, 48, 5, 245, 57],
    [188, 195, 30, 98, 161, 141, 24, 190, 76, 246, 82, 9, 10, 64, 77, 155, 142, 155, 226, 42, 254, 235, 45, 75, 78, 226, 226, 82, 213, 64, 147, 111],
    [18, 224, 77, 129, 141, 59, 109, 251, 253, 71, 211, 186, 75, 89, 8, 210, 4, 107, 68, 58, 126, 92, 108, 234, 8, 68, 65, 185, 112, 113, 191, 176],
    [203, 150, 60, 77, 15, 7, 62, 123, 167, 92, 232, 120, 10, 180, 41, 158, 151, 47, 180, 123, 48, 125, 246, 163, 175, 77, 233, 178, 175, 80, 132, 69],
    [13, 80, 180, 250, 156, 162, 176, 222, 76, 178, 89, 5, 82, 119, 40, 133, 132, 171, 52, 32, 78, 139, 203, 134, 91, 4, 57, 14, 251, 83, 95, 241],
    [121, 139, 246, 69, 116, 41, 78, 169, 210, 22, 10, 86, 163, 250, 216, 95, 60, 84, 77, 149, 46, 219, 186, 154, 99, 16, 168, 136, 154, 230, 221, 36],
    [27, 66, 52, 241, 37, 168, 22, 252, 114, 218, 26, 217, 217, 105, 24, 77, 183, 134, 132, 192, 153, 233, 12, 3, 47, 223, 158, 132, 142, 82, 223, 118],
    [59, 109, 76, 24, 23, 102, 102, 140, 51, 58, 196, 75, 42, 213, 236, 84, 97, 187, 162, 219, 133, 154, 148, 104, 188, 128, 93, 78, 151, 241, 145, 14],
    [164, 204, 223, 177, 22, 233, 125, 95, 232, 30, 13, 87, 1, 184, 124, 54, 199, 220, 242, 121, 125, 112, 239, 92, 70, 8, 186, 89, 248, 14, 171, 57],
    [4, 92, 89, 202, 44, 223, 191, 204, 253, 3, 143, 243, 154, 27, 204, 200, 158, 102, 130, 206, 127, 42, 214, 68, 210, 95, 61, 71, 100, 164, 254, 69],
    [228, 135, 138, 5, 26, 91, 162, 69, 106, 142, 190, 201, 196, 84, 229, 189, 203, 16, 164, 69, 17, 215, 151, 47, 43, 38, 241, 227, 34, 181, 169, 84],
    [124, 123, 135, 232, 23, 109, 240, 80, 116, 168, 195, 138, 117, 75, 179, 39, 87, 196, 201, 254, 204, 98, 185, 28, 179, 144, 111, 132, 200, 52, 64, 69],
    [230, 21, 211, 248, 172, 195, 12, 66, 88, 136, 95, 14, 117, 120, 213, 232, 215, 47, 188, 1, 33, 41, 162, 59, 130, 150, 7, 161, 196, 101, 137, 83],
    [30, 186, 53, 17, 199, 144, 155, 172, 178, 77, 97, 68, 229, 249, 236, 252, 165, 214, 208, 146, 10, 110, 38, 128, 244, 235, 239, 6, 217, 169, 202, 207],
    [163, 154, 255, 216, 217, 82, 190, 47, 199, 240, 15, 212, 148, 128, 140, 70, 112, 96, 145, 96, 121, 108, 31, 241, 95, 201, 243, 185, 96, 18, 138, 40],
    [183, 48, 151, 238, 109, 129, 246, 173, 15, 82, 66, 194, 145, 250, 25, 36, 23, 156, 211, 245, 213, 116, 90, 158, 180, 241, 253, 227, 142, 36, 146, 126],
    [132, 84, 4, 48, 37, 208, 111, 33, 50, 248, 79, 118, 181, 211, 239, 60, 152, 221, 128, 2, 57, 190, 48, 193, 171, 77, 154, 244, 223, 149, 64, 230],
    [72, 238, 4, 130, 85, 234, 140, 98, 165, 254, 132, 91, 91, 99, 183, 108, 195, 178, 115, 43, 221, 93, 148, 227, 196, 253, 62, 58, 173, 110, 195, 142],
    [112, 12, 216, 34, 243, 115, 85, 92, 229, 72, 35, 54, 86, 235, 50, 122, 222, 26, 64, 95, 239, 204, 99, 61, 219, 169, 32, 180, 48, 63, 115, 47],
    [168, 1, 135, 186, 168, 171, 173, 224, 94, 119, 81, 51, 22, 213, 114, 191, 216, 31, 162, 176, 141, 124, 121, 113, 144, 198, 86, 225, 4, 50, 201, 124],
    [41, 50, 15, 15, 136, 184, 31, 172, 36, 74, 50, 170, 169, 159, 246, 245, 181, 96, 158, 186, 24, 204, 5, 211, 5, 215, 238, 213, 198, 179, 128, 67],
    [249, 246, 135, 211, 191, 12, 26, 173, 162, 65, 93, 94, 154, 130, 197, 113, 165, 49, 33, 88, 172, 137, 132, 74, 209, 57, 49, 164, 205, 158, 210, 21],
    [40, 181, 199, 200, 60, 225, 129, 107, 27, 134, 49, 222, 212, 155, 69, 148, 39, 163, 175, 11, 189, 235, 171, 91, 136, 1, 138, 113, 112, 228, 20, 159],
    [77, 242, 127, 14, 98, 114, 180, 157, 138, 18, 99, 205, 66, 89, 51, 14, 153, 69, 110, 216, 60, 109, 207, 83, 204, 210, 154, 156, 220, 242, 108, 127],
    [43, 141, 129, 45, 18, 142, 251, 180, 152, 202, 205, 42, 132, 121, 245, 230, 98, 6, 201, 203, 237, 154, 70, 72, 126, 29, 134, 163, 254, 153, 165, 170],
    [211, 88, 196, 127, 190, 31, 156, 212, 147, 4, 167, 39, 48, 204, 42, 247, 198, 148, 192, 128, 209, 2, 155, 235, 191, 227, 198, 40, 35, 28, 184, 197],
    [247, 144, 22, 199, 135, 136, 210, 180, 33, 236, 104, 124, 149, 2, 28, 13, 185, 206, 104, 130, 232, 117, 119, 147, 71, 171, 45, 157, 69, 45, 168, 218],
    [32, 27, 235, 22, 40, 136, 240, 130, 104, 86, 216, 83, 59, 168, 155, 223, 246, 121, 0, 133, 41, 10, 247, 227, 172, 30, 24, 5, 54, 213, 59, 242],
    [64, 124, 244, 138, 131, 107, 118, 226, 160, 137, 66, 9, 206, 178, 47, 101, 23, 172, 206, 253, 122, 153, 143, 132, 193, 136, 213, 136, 27, 143, 127, 203],
    [39, 237, 56, 45, 153, 102, 149, 249, 183, 202, 95, 78, 73, 119, 227, 30, 253, 159, 124, 82, 238, 66, 162, 54, 223, 5, 10, 150, 173, 65, 79, 116],
    [183, 148, 96, 103, 119, 79, 117, 84, 212, 78, 54, 145, 48, 254, 194, 205, 20, 72, 0, 146, 117, 218, 160, 211, 28, 155, 188, 187, 86, 212, 161, 150],
    [22, 158, 134, 220, 136, 200, 70, 229, 12, 218, 15, 87, 182, 79, 75, 117, 137, 128, 119, 243, 246, 193, 90, 26, 189, 157, 184, 222, 121, 195, 211, 236],
    [80, 42, 174, 200, 28, 114, 206, 124, 126, 196, 11, 122, 136, 123, 205, 205, 140, 113, 69, 213, 166, 140, 247, 21, 46, 149, 246, 89, 11, 79, 255, 238],
    [19, 95, 99, 184, 7, 22, 194, 86, 129, 13, 32, 210, 230, 211, 255, 75, 187, 8, 249, 158, 205, 206, 27, 168, 158, 184, 136, 94, 137, 55, 165, 19],
    [9, 204, 255, 83, 244, 172, 118, 86, 159, 25, 5, 26, 81, 88, 146, 124, 96, 10, 60, 88, 25, 18, 185, 48, 135, 63, 99, 229, 206, 76, 12, 224],
    [109, 253, 187, 146, 148, 71, 251, 162, 170, 112, 207, 170, 19, 197, 159, 34, 228, 192, 7, 55, 4, 86, 223, 124, 225, 101, 40, 18, 84, 22, 38, 36],
    [103, 43, 238, 144, 166, 210, 219, 243, 173, 100, 26, 208, 172, 187, 193, 195, 182, 136, 18, 252, 18, 186, 88, 122, 143, 223, 21, 58, 96, 20, 218, 1],
    [74, 128, 8, 181, 212, 144, 163, 4, 70, 27, 203, 81, 107, 8, 44, 226, 63, 181, 5, 88, 232, 101, 90, 206, 218, 98, 154, 184, 168, 47, 198, 142],
    [163, 36, 157, 139, 213, 17, 14, 174, 237, 67, 144, 187, 39, 222, 233, 212, 185, 7, 110, 135, 216, 43, 205, 106, 48, 206, 190, 1, 166, 120, 100, 120],
    [70, 148, 185, 147, 253, 105, 153, 236, 131, 97, 177, 34, 250, 143, 243, 25, 97, 198, 230, 168, 105, 37, 47, 121, 31, 120, 63, 103, 204, 60, 16, 98],
    [71, 94, 10, 25, 14, 45, 19, 239, 40, 196, 66, 166, 63, 205, 162, 63, 26, 166, 204, 46, 128, 52, 25, 200, 80, 238, 92, 20, 210, 122, 20, 52],
    [233, 229, 183, 84, 114, 241, 140, 254, 61, 164, 42, 238, 192, 104, 211, 131, 112, 230, 105, 159, 179, 170, 107, 99, 55, 42, 64, 0, 154, 43, 249, 94],
    [76, 69, 22, 4, 128, 17, 68, 143, 247, 3, 52, 50, 230, 249, 23, 119, 33, 160, 131, 53, 127, 251, 166, 165, 50, 193, 163, 126, 56, 223, 192, 200],
    [192, 220, 174, 230, 230, 181, 109, 112, 103, 70, 49, 35, 251, 104, 70, 157, 0, 136, 56, 47, 235, 172, 128, 26, 190, 192, 3, 238, 74, 161, 93, 12],
    [217, 254, 39, 243, 216, 7, 167, 196, 100, 103, 50, 95, 113, 137, 73, 94, 130, 176, 153, 206, 46, 20, 197, 177, 108, 199, 102, 151, 250, 144, 159, 129],
    [65, 237, 236, 228, 45, 99, 232, 217, 191, 81, 90, 155, 166, 147, 46, 28, 32, 203, 201, 245, 165, 209, 52, 100, 90, 219, 93, 177, 185, 115, 126, 163],
    [187, 3, 129, 193, 62, 8, 23, 32, 19, 85, 231, 215, 0, 183, 98, 63, 14, 152, 82, 135, 173, 215, 135, 18, 161, 20, 7, 201, 247, 84, 239, 200],
    [117, 61, 155, 160, 127, 40, 203, 22, 182, 209, 140, 189, 47, 64, 111, 155, 96, 157, 94, 150, 89, 0, 228, 56, 42, 154, 138, 85, 189, 14, 74, 65],
    [147, 24, 17, 222, 126, 247, 160, 94, 186, 12, 199, 194, 76, 13, 223, 222, 95, 229, 218, 222, 14, 22, 14, 56, 184, 220, 130, 27, 187, 27, 146, 146],
    [228, 154, 232, 205, 185, 157, 58, 87, 155, 221, 115, 105, 15, 88, 104, 207, 137, 47, 59, 181, 111, 18, 110, 186, 106, 136, 136, 139, 31, 35, 42, 252],
    [159, 226, 188, 108, 202, 160, 83, 252, 189, 15, 17, 232, 52, 52, 162, 113, 125, 115, 229, 225, 53, 147, 170, 202, 234, 64, 103, 110, 135, 74, 61, 138],
    [50, 189, 145, 4, 101, 249, 202, 35, 32, 181, 94, 10, 69, 253, 123, 151, 1, 77, 43, 67, 12, 88, 175, 39, 209, 101, 165, 71, 251, 68, 54, 105],
    [77, 160, 234, 167, 231, 135, 92, 84, 79, 70, 36, 240, 237, 239, 225, 167, 13, 92, 212, 214, 85, 237, 229, 142, 207, 114, 56, 100, 135, 211, 38, 168],
    [20, 175, 218, 158, 176, 170, 147, 148, 135, 162, 92, 99, 158, 229, 236, 81, 124, 10, 186, 120, 159, 90, 167, 115, 180, 48, 151, 236, 50, 104, 78, 66],
    [139, 23, 99, 49, 119, 193, 92, 225, 153, 127, 4, 223, 150, 105, 26, 165, 48, 105, 171, 196, 233, 24, 189, 172, 30, 164, 224, 101, 43, 195, 202, 165],
    [105, 77, 36, 198, 130, 131, 185, 154, 213, 238, 92, 234, 163, 93, 157, 228, 221, 85, 69, 221, 122, 56, 95, 75, 24, 250, 133, 178, 220, 109, 226, 186],
    [212, 118, 206, 1, 195, 120, 123, 202, 176, 84, 162, 207, 72, 214, 175, 109, 211, 3, 160, 235, 84, 158, 33, 167, 65, 37, 19, 47, 121, 217, 12, 54],
    [10, 70, 91, 204, 238, 238, 65, 100, 251, 107, 196, 224, 8, 103, 180, 164, 117, 50, 38, 89, 17, 208, 155, 240, 136, 52, 62, 36, 240, 136, 58, 54],
    [118, 2, 245, 88, 143, 145, 181, 12, 96, 227, 103, 130, 21, 212, 184, 98, 198, 65, 27, 242, 232, 218, 63, 57, 2, 7, 126, 152, 85, 6, 176, 235],
    [165, 197, 223, 103, 233, 137, 96, 169, 167, 129, 111, 219, 30, 249, 151, 11, 84, 139, 66, 82, 101, 240, 141, 54, 0, 156, 70, 51, 56, 114, 98, 147],
    [218, 190, 74, 210, 232, 225, 50, 99, 102, 43, 63, 154, 195, 10, 222, 127, 23, 111, 247, 207, 30, 254, 26, 252, 31, 164, 217, 162, 26, 153, 118, 250],
    [53, 98, 145, 84, 31, 117, 211, 72, 223, 38, 200, 116, 216, 212, 253, 154, 236, 129, 80, 81, 60, 118, 140, 148, 175, 52, 160, 111, 208, 52, 2, 85],
    [236, 188, 74, 117, 38, 98, 25, 209, 42, 248, 106, 124, 191, 220, 29, 128, 59, 178, 155, 1, 37, 136, 253, 70, 139, 106, 140, 221, 139, 52, 44, 90],
    [202, 25, 203, 206, 82, 222, 52, 29, 100, 198, 155, 225, 153, 86, 248, 176, 215, 109, 70, 253, 224, 88, 39, 119, 247, 136, 25, 97, 39, 24, 252, 84],
    [82, 57, 81, 1, 241, 94, 200, 116, 30, 79, 9, 99, 151, 18, 64, 129, 231, 221, 137, 159, 51, 204, 169, 71, 65, 185, 116, 32, 211, 206, 67, 146],
    [164, 107, 195, 32, 250, 166, 96, 158, 93, 117, 233, 72, 34, 203, 163, 73, 184, 18, 159, 242, 115, 53, 84, 116, 32, 172, 252, 34, 247, 37, 69, 187],
    [172, 7, 30, 136, 254, 71, 229, 72, 47, 65, 159, 147, 243, 46, 85, 160, 199, 139, 30, 122, 252, 96, 251, 93, 112, 191, 160, 177, 85, 217, 107, 231],
    [232, 11, 239, 215, 249, 36, 191, 89, 139, 135, 60, 55, 147, 165, 86, 47, 160, 190, 176, 192, 5, 51, 120, 221, 155, 164, 180, 139, 129, 169, 158, 213],
    [188, 33, 178, 133, 31, 60, 101, 5, 66, 251, 206, 76, 32, 200, 118, 6, 67, 131, 225, 200, 234, 26, 90, 56, 92, 234, 54, 45, 247, 78, 127, 64],
    [46, 220, 152, 104, 71, 226, 9, 180, 1, 110, 20, 26, 109, 200, 113, 109, 50, 7, 53, 15, 65, 105, 105, 56, 45, 67, 21, 57, 191, 41, 46, 74],
    
    ];

    #[test]
    fn hash_variable_len_bytes() {
		let mut sha256 = Sha256::new();
        for i in 0..HASHES.len() {
            let mut message_bytes = Vec::<u8>::new();
            for _ in 0..=i {
                message_bytes.push(97); // 'a'
            }
            println!("testing msg of len {}", message_bytes.len());
            let hash = sha256.digest(&message_bytes);
            println!("hash: {:?}", hash);
            println!("expected: {:?}", HASHES[i]);
            assert_eq!(hash, HASHES[i], "hashes[{}] with {}x'a'", i, i+1);
        }
    }

    #[test]
    fn hash_variable_len_bytes_shuffled() {
        // deliberately shuffle the test cases to avoid any potential order dependency

        let mut rng = Rng::new(0);

        let limit = 10_000;
        let mut count: usize = 0;
        let mut sha256 = Sha256::new();
        loop {
            let mut message_bytes = Vec::<u8>::new();
            let i = (rng.next() % HASHES.len() as u64) as usize;
            println!("i {}", i);
            for _ in 0..=i {
                message_bytes.push(97); // 'a'
            }
            println!("testing msg of len {}", message_bytes.len());
            let hash = sha256.digest(&message_bytes);
            println!("hash: {:?}", hash);
            println!("expected: {:?}", HASHES[i]);
            assert_eq!(hash, HASHES[i], "hashes[{}] with {}x'a'", i, i+1);

            count += 1;
            if count == limit {
                break;            
            }
        }
        println!("total test cases: {}", count);
    }

}