diff --git a/provers/cairo/src/air.rs b/provers/cairo/src/air.rs index df007c696..e4f5611a6 100644 --- a/provers/cairo/src/air.rs +++ b/provers/cairo/src/air.rs @@ -560,6 +560,7 @@ fn generate_memory_permutation_argument_column( }) .collect::>() } + fn generate_range_check_permutation_argument_column( offset_column_original: &[Felt252], offset_column_sorted: &[Felt252], @@ -881,30 +882,31 @@ fn compute_instr_constraints(constraints: &mut [Felt252], frame: &Frame = (0..16) .map(|col_idx| curr.get_evaluation_element(0, col_idx)) .collect(); - // Bit constraints - for (i, flag) in flags.clone().into_iter().enumerate() { - constraints[i] = match i { - 0..=14 => flag * (flag - Felt252::one()), - 15 => *flag, + let two = Felt252::from(2); + (0..15).for_each(|idx| { + constraints[idx] = match idx { + 0..=14 => { + (flags[idx] - two * flags[idx + 1]) + * (flags[idx] - two * flags[idx + 1] - Felt252::one()) + } + 15 => *flags[idx], _ => panic!("Unknown flag offset"), - }; - } + } + }); // Instruction unpacking - let two = Felt252::from(2); let b16 = two.pow(16u32); let b32 = two.pow(32u32); let b48 = two.pow(48u32); // Named like this to match the Cairo whitepaper's notation. - let f0_squiggle = flags - .into_iter() - .rev() - .fold(Felt252::zero(), |acc, flag| flag + two * acc); + let f0_squiggle = flags[0]; let off_dst = curr.get_evaluation_element(0, OFF_DST); let off_op0 = curr.get_evaluation_element(0, OFF_OP0); @@ -922,17 +924,17 @@ fn compute_operand_constraints(constraints: &mut [Felt252], frame: &Frame, element_idx: usize) -> Felt252 { + step.get_evaluation_element(0, element_idx) + - Felt252::from(2) * step.get_evaluation_element(0, element_idx + 1) +} + fn compute_register_constraints(constraints: &mut [Felt252], frame: &Frame) { let curr = frame.get_evaluation_step(0); let next = frame.get_evaluation_step(1); @@ -961,25 +971,25 @@ fn compute_register_constraints(constraints: &mut [Felt252], frame: &Frame) -> Felt252 { - let op1_val = step.get_evaluation_element(0, F_OP_1_VAL); + let op1_val = into_bit_flag(step, F_OP_1_VAL); op1_val + Felt252::one() } diff --git a/provers/cairo/src/decode/instruction_flags.rs b/provers/cairo/src/decode/instruction_flags.rs index 71b23e2a1..d049e6ee9 100644 --- a/provers/cairo/src/decode/instruction_flags.rs +++ b/provers/cairo/src/decode/instruction_flags.rs @@ -53,14 +53,14 @@ impl CairoInstructionFlags { /// represented by field elements: Felt252::zero() for bit 0 and /// Felt252::one() for bit 1. #[rustfmt::skip] - pub fn to_trace_representation(&self) -> [Felt252; 16] { - let b0 = self.dst_reg.to_trace_representation(); - let b1 = self.op0_reg.to_trace_representation(); - let [b2, b3, b4] = self.op1_src.to_trace_representation(); - let [b5, b6] = self.res_logic.to_trace_representation(); - let [b7, b8, b9] = self.pc_update.to_trace_representation(); - let [b10, b11] = self.ap_update.to_trace_representation(); - let [b12, b13, b14] = self.opcode.to_trace_representation(); + pub fn to_bit_representation(&self) -> [Felt252; 16] { + let b0 = self.dst_reg.to_bit_representation(); + let b1 = self.op0_reg.to_bit_representation(); + let [b2, b3, b4] = self.op1_src.to_bit_representation(); + let [b5, b6] = self.res_logic.to_bit_representation(); + let [b7, b8, b9] = self.pc_update.to_bit_representation(); + let [b10, b11] = self.ap_update.to_bit_representation(); + let [b12, b13, b14] = self.opcode.to_bit_representation(); // In the paper, a little-endian format for the bit flags is // mentioned. That is why they are arranged in this way (section 4.4 @@ -76,6 +76,11 @@ impl CairoInstructionFlags { Felt252::zero(), ] } + + pub fn to_trace_representation(&self) -> [Felt252; 16] { + let bit_flags = self.to_bit_representation(); + to_bit_prefixes(bit_flags) + } } #[derive(Debug, PartialEq, Eq, Clone)] @@ -85,7 +90,7 @@ pub enum Op0Reg { } impl Op0Reg { - pub fn to_trace_representation(&self) -> Felt252 { + pub fn to_bit_representation(&self) -> Felt252 { match self { Op0Reg::AP => Felt252::zero(), Op0Reg::FP => Felt252::one(), @@ -117,7 +122,7 @@ pub enum DstReg { FP = 1, } impl DstReg { - pub fn to_trace_representation(&self) -> Felt252 { + pub fn to_bit_representation(&self) -> Felt252 { match self { DstReg::AP => Felt252::zero(), DstReg::FP => Felt252::one(), @@ -151,7 +156,7 @@ pub enum Op1Src { } impl Op1Src { - pub fn to_trace_representation(&self) -> [Felt252; 3] { + pub fn to_bit_representation(&self) -> [Felt252; 3] { match self { Op1Src::Op0 => [Felt252::zero(), Felt252::zero(), Felt252::zero()], Op1Src::Imm => [Felt252::zero(), Felt252::zero(), Felt252::one()], @@ -188,7 +193,7 @@ pub enum ResLogic { } impl ResLogic { - pub fn to_trace_representation(&self) -> [Felt252; 2] { + pub fn to_bit_representation(&self) -> [Felt252; 2] { match self { ResLogic::Op1 => [Felt252::zero(), Felt252::zero()], ResLogic::Add => [Felt252::zero(), Felt252::one()], @@ -225,7 +230,7 @@ pub enum PcUpdate { } impl PcUpdate { - pub fn to_trace_representation(&self) -> [Felt252; 3] { + pub fn to_bit_representation(&self) -> [Felt252; 3] { match self { PcUpdate::Regular => [Felt252::zero(), Felt252::zero(), Felt252::zero()], PcUpdate::Jump => [Felt252::zero(), Felt252::zero(), Felt252::one()], @@ -262,7 +267,7 @@ pub enum ApUpdate { } impl ApUpdate { - pub fn to_trace_representation(&self) -> [Felt252; 2] { + pub fn to_bit_representation(&self) -> [Felt252; 2] { match self { ApUpdate::Regular => [Felt252::zero(), Felt252::zero()], ApUpdate::Add => [Felt252::zero(), Felt252::one()], @@ -314,7 +319,7 @@ pub enum CairoOpcode { } impl CairoOpcode { - pub fn to_trace_representation(&self) -> [Felt252; 3] { + pub fn to_bit_representation(&self) -> [Felt252; 3] { match self { CairoOpcode::NOp => [Felt252::zero(), Felt252::zero(), Felt252::zero()], CairoOpcode::Call => [Felt252::zero(), Felt252::zero(), Felt252::one()], @@ -341,6 +346,28 @@ impl TryFrom<&Felt252> for CairoOpcode { } } +fn to_bit_prefixes(bit_array: [Felt252; 16]) -> [Felt252; 16] { + let two = Felt252::from(2); + (0..bit_array.len()) + .map(|i| { + bit_array + .iter() + .enumerate() + .fold(Felt252::zero(), |acc, (j, flag_j)| { + let sum_term = if j < i { + Felt252::zero() + } else { + let exponent = j - i; + two.pow(exponent) * flag_j + }; + acc + sum_term + }) + }) + .collect::>() + .try_into() + .unwrap() +} + #[cfg(test)] mod tests { use super::*; @@ -671,7 +698,7 @@ mod tests { } #[test] - fn flags_trace_representation() { + fn flags_bit_representation() { // Bit-trace representation for each flag: // DstReg::FP = 1 // Op0Reg::FP = 1 @@ -703,8 +730,42 @@ mod tests { Felt252::zero(), ]; - let representation = flags.to_trace_representation(); + let representation = flags.to_bit_representation(); assert_eq!(representation, expected_representation); } + + #[test] + fn to_bit_prefixes_all_zeros_works() { + let bit_array = [Felt252::zero(); 16]; + + let result = to_bit_prefixes(bit_array); + let expected = [Felt252::zero(); 16]; + + assert_eq!(result, expected); + } + + #[test] + fn to_bit_prefixes_flag14_on_works() { + let mut bit_array = [Felt252::zero(); 16]; + // We turn on only the 14th bit, which is the most significant. + + bit_array[14] = Felt252::one(); + + let result = to_bit_prefixes(bit_array); + // The bit prefix value of f0 should be 16384, and the rest + // should be the bit prefixes of that number. + let expected: [Felt252; 16] = (0..16u32) + .map(|idx| { + if idx == 15 { + return Felt252::zero(); + } + Felt252::from(16384) / Felt252::from(2).pow(idx) + }) + .collect::>() + .try_into() + .unwrap(); + + assert_eq!(result, expected); + } } diff --git a/provers/cairo/src/execution_trace.rs b/provers/cairo/src/execution_trace.rs index 00cd76c5d..c67eb7cff 100644 --- a/provers/cairo/src/execution_trace.rs +++ b/provers/cairo/src/execution_trace.rs @@ -194,14 +194,14 @@ fn fill_memory_holes(trace: &mut CairoTraceTable, memory_holes: &[Felt252]) { /// The constraints of the Cairo AIR are defined over this trace rather than the raw trace /// obtained from the Cairo VM, this is why this function is needed. pub fn build_cairo_execution_trace( - raw_trace: &RegisterStates, + register_states: &RegisterStates, memory: &CairoMemory, ) -> CairoTraceTable { - let n_steps = raw_trace.steps(); + let n_steps = register_states.steps(); // Instruction flags and offsets are decoded from the raw instructions and represented // by the CairoInstructionFlags and InstructionOffsets as an intermediate representation - let (flags, offsets): (Vec, Vec) = raw_trace + let (flags, offsets): (Vec, Vec) = register_states .flags_and_offsets(memory) .unwrap() .into_iter() @@ -209,15 +209,15 @@ pub fn build_cairo_execution_trace( // dst, op0, op1 and res are computed from flags and offsets let (dst_addrs, mut dsts): (Vec, Vec) = - compute_dst(&flags, &offsets, raw_trace, memory); + compute_dst(&flags, &offsets, register_states, memory); let (op0_addrs, mut op0s): (Vec, Vec) = - compute_op0(&flags, &offsets, raw_trace, memory); + compute_op0(&flags, &offsets, register_states, memory); let (op1_addrs, op1s): (Vec, Vec) = - compute_op1(&flags, &offsets, raw_trace, memory, &op0s); + compute_op1(&flags, &offsets, register_states, memory, &op0s); let mut res = compute_res(&flags, &op0s, &op1s, &dsts); // In some cases op0, dst or res may need to be updated from the already calculated values - update_values(&flags, raw_trace, &mut op0s, &mut dsts, &mut res); + update_values(&flags, register_states, &mut op0s, &mut dsts, &mut res); // Flags and offsets are transformed to a bit representation. This is needed since // the flag constraints of the Cairo AIR are defined over bit representations of these @@ -231,10 +231,22 @@ pub fn build_cairo_execution_trace( .collect(); // ap, fp, pc and instruction columns are computed - let aps: Vec = raw_trace.rows.iter().map(|t| Felt252::from(t.ap)).collect(); - let fps: Vec = raw_trace.rows.iter().map(|t| Felt252::from(t.fp)).collect(); - let pcs: Vec = raw_trace.rows.iter().map(|t| Felt252::from(t.pc)).collect(); - let instructions: Vec = raw_trace + let aps: Vec = register_states + .rows + .iter() + .map(|t| Felt252::from(t.ap)) + .collect(); + let fps: Vec = register_states + .rows + .iter() + .map(|t| Felt252::from(t.fp)) + .collect(); + let pcs: Vec = register_states + .rows + .iter() + .map(|t| Felt252::from(t.pc)) + .collect(); + let instructions: Vec = register_states .rows .iter() .map(|t| *memory.get(&t.pc).unwrap()) @@ -242,10 +254,11 @@ pub fn build_cairo_execution_trace( // t0, t1 and mul derived values are constructed. For details reFelt252r to // section 9.1 of the Cairo whitepaper + let two = Felt252::from(2); let t0: Vec = trace_repr_flags .iter() .zip(&dsts) - .map(|(repr_flags, dst)| repr_flags[9] * dst) + .map(|(repr_flags, dst)| (repr_flags[9] - two * repr_flags[10]) * dst) .collect(); let t1: Vec = t0.iter().zip(&res).map(|(t, r)| t * r).collect(); let mul: Vec = op0s.iter().zip(&op1s).map(|(op0, op1)| op0 * op1).collect(); diff --git a/provers/cairo/src/main.rs b/provers/cairo/src/main.rs index b0ae341b4..2139a0953 100644 --- a/provers/cairo/src/main.rs +++ b/provers/cairo/src/main.rs @@ -214,6 +214,8 @@ fn write_proof( bytes.extend(proof_bytes); bytes.extend(pub_inputs_bytes); + println!("PROOF: {:?}", bytes); + let Ok(()) = std::fs::write(&proof_path, bytes) else { eprintln!("Error writing proof to file: {}", &proof_path); return; diff --git a/provers/cairo/tests/wasm.rs b/provers/cairo/tests/wasm.rs index f1b1ebebc..dc25be9da 100644 --- a/provers/cairo/tests/wasm.rs +++ b/provers/cairo/tests/wasm.rs @@ -20,1217 +20,1218 @@ fn test_prove_cairo1_program_wasm() { // Test case is fibo5, with default test options #[cfg(feature = "wasm")] static PROOF: [u8; 25388] = [ - 187, 90, 0, 0, 64, 2, 197, 227, 209, 214, 234, 176, 74, 98, 199, 182, 19, 90, 139, 127, 49, 93, - 25, 39, 21, 35, 201, 171, 91, 133, 169, 200, 141, 63, 81, 247, 79, 170, 14, 38, 34, 55, 254, - 17, 175, 19, 60, 237, 160, 79, 46, 154, 30, 180, 252, 42, 68, 142, 77, 86, 111, 139, 242, 3, - 226, 1, 95, 218, 239, 63, 118, 32, 7, 24, 54, 199, 244, 240, 99, 243, 112, 72, 26, 216, 16, 72, - 7, 251, 141, 117, 5, 214, 60, 81, 254, 137, 142, 149, 33, 30, 71, 216, 189, 119, 32, 7, 222, - 169, 28, 15, 92, 178, 160, 254, 171, 153, 255, 147, 86, 140, 34, 24, 230, 88, 10, 154, 115, - 134, 17, 74, 180, 117, 123, 115, 126, 11, 51, 32, 1, 185, 123, 144, 24, 143, 85, 5, 128, 214, - 220, 172, 126, 90, 233, 112, 7, 76, 231, 25, 251, 175, 98, 25, 202, 159, 110, 124, 178, 156, - 193, 21, 32, 4, 219, 214, 196, 63, 204, 107, 225, 143, 71, 131, 182, 214, 41, 97, 3, 190, 103, - 201, 177, 137, 70, 147, 194, 153, 248, 50, 202, 255, 62, 95, 221, 32, 1, 106, 173, 171, 167, - 164, 61, 9, 239, 225, 159, 156, 171, 123, 181, 140, 58, 75, 79, 52, 123, 10, 10, 35, 155, 104, - 94, 184, 78, 36, 222, 239, 32, 6, 90, 128, 110, 216, 52, 115, 62, 170, 100, 34, 192, 147, 42, - 32, 240, 144, 221, 29, 28, 73, 147, 192, 90, 178, 152, 171, 156, 36, 254, 89, 99, 32, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, - 58, 255, 2, 204, 42, 213, 16, 211, 193, 7, 27, 66, 237, 136, 203, 211, 141, 218, 142, 185, 237, - 62, 103, 205, 25, 129, 31, 154, 128, 230, 175, 32, 0, 240, 205, 76, 65, 68, 43, 246, 122, 251, - 182, 180, 141, 3, 29, 31, 103, 20, 103, 180, 144, 191, 138, 86, 138, 172, 247, 220, 219, 173, - 95, 129, 32, 1, 130, 83, 75, 132, 173, 0, 202, 89, 51, 149, 147, 244, 175, 64, 81, 83, 210, - 189, 134, 146, 52, 170, 95, 247, 34, 205, 79, 223, 241, 243, 148, 32, 4, 139, 110, 17, 83, 119, - 173, 113, 201, 172, 45, 116, 184, 81, 149, 156, 230, 25, 174, 1, 196, 253, 5, 89, 244, 247, - 101, 86, 126, 58, 120, 97, 32, 0, 26, 216, 193, 81, 133, 61, 144, 95, 89, 100, 237, 91, 7, 83, - 88, 96, 20, 9, 177, 63, 81, 50, 70, 202, 114, 66, 232, 220, 220, 75, 223, 32, 0, 33, 86, 227, - 240, 163, 75, 80, 1, 84, 102, 0, 108, 169, 115, 221, 231, 25, 167, 245, 101, 140, 121, 238, - 181, 75, 138, 132, 140, 129, 244, 174, 32, 0, 58, 255, 2, 204, 42, 213, 16, 211, 193, 7, 27, - 66, 237, 136, 203, 211, 141, 218, 142, 185, 237, 62, 103, 205, 25, 129, 31, 154, 128, 230, 175, - 32, 0, 198, 114, 84, 26, 108, 78, 173, 142, 99, 127, 39, 131, 14, 132, 38, 139, 113, 82, 52, - 94, 33, 135, 135, 188, 31, 84, 93, 43, 165, 77, 188, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 2, 152, 174, 215, 120, 114, 172, - 71, 249, 37, 75, 41, 62, 28, 117, 68, 130, 163, 209, 122, 163, 114, 173, 150, 1, 121, 139, 209, - 47, 22, 114, 248, 32, 4, 22, 55, 152, 30, 133, 3, 245, 123, 81, 233, 247, 229, 12, 103, 213, - 26, 100, 142, 154, 26, 140, 34, 90, 72, 93, 63, 85, 123, 189, 33, 26, 32, 0, 51, 12, 228, 110, - 35, 73, 215, 141, 141, 204, 177, 79, 138, 122, 213, 229, 236, 2, 18, 178, 122, 254, 89, 20, 46, - 11, 135, 88, 205, 5, 144, 32, 6, 90, 176, 69, 190, 22, 5, 102, 86, 216, 93, 81, 81, 98, 113, - 161, 7, 159, 60, 66, 102, 68, 27, 135, 164, 102, 178, 228, 145, 203, 162, 115, 32, 0, 132, 141, - 86, 182, 112, 140, 202, 9, 69, 56, 99, 10, 70, 67, 50, 17, 115, 18, 50, 12, 36, 246, 247, 113, - 123, 65, 84, 190, 3, 8, 194, 32, 4, 207, 223, 178, 180, 228, 40, 165, 199, 189, 127, 19, 204, - 228, 153, 167, 82, 67, 1, 45, 240, 98, 29, 243, 103, 65, 191, 175, 11, 91, 141, 55, 32, 5, 103, - 186, 10, 176, 89, 226, 140, 32, 253, 199, 160, 225, 107, 143, 21, 228, 172, 134, 101, 200, 157, - 199, 55, 101, 173, 162, 136, 73, 174, 160, 28, 32, 4, 193, 125, 59, 169, 62, 158, 88, 108, 202, - 77, 18, 248, 111, 89, 61, 171, 126, 89, 83, 165, 226, 61, 250, 81, 77, 58, 218, 144, 24, 143, - 114, 32, 5, 161, 183, 168, 127, 116, 230, 158, 52, 196, 110, 121, 230, 118, 12, 61, 45, 75, - 143, 91, 234, 176, 194, 255, 150, 120, 251, 73, 35, 217, 16, 94, 32, 5, 171, 109, 157, 208, 78, - 232, 92, 70, 200, 192, 32, 29, 49, 177, 87, 141, 38, 0, 207, 3, 143, 188, 254, 28, 30, 25, 86, - 71, 137, 238, 202, 32, 6, 38, 1, 31, 140, 127, 24, 84, 225, 32, 159, 36, 165, 108, 17, 50, 66, - 101, 60, 86, 95, 20, 72, 128, 6, 152, 8, 97, 64, 130, 49, 129, 32, 4, 252, 138, 11, 107, 147, - 180, 107, 218, 133, 152, 170, 155, 100, 189, 199, 203, 250, 92, 10, 198, 135, 25, 13, 196, 94, - 177, 174, 14, 233, 114, 215, 32, 0, 146, 26, 157, 222, 99, 150, 41, 30, 88, 91, 121, 93, 124, - 51, 89, 238, 39, 53, 252, 110, 141, 92, 109, 24, 207, 127, 163, 78, 167, 59, 146, 32, 4, 37, - 194, 48, 45, 133, 170, 208, 223, 56, 163, 233, 151, 134, 148, 172, 19, 192, 177, 151, 14, 72, - 185, 255, 147, 58, 105, 62, 232, 204, 55, 211, 32, 7, 229, 14, 78, 104, 253, 195, 18, 234, 32, - 251, 164, 28, 163, 155, 251, 4, 225, 55, 137, 98, 160, 117, 215, 113, 200, 76, 79, 98, 28, 142, - 172, 32, 0, 246, 92, 64, 233, 215, 202, 157, 11, 200, 108, 83, 191, 54, 151, 124, 52, 238, 89, - 4, 128, 83, 20, 69, 55, 73, 126, 192, 230, 207, 149, 175, 32, 2, 91, 133, 33, 130, 142, 30, 26, - 129, 191, 201, 220, 24, 7, 140, 212, 59, 107, 188, 127, 147, 200, 191, 91, 168, 84, 92, 64, 82, - 187, 88, 33, 32, 4, 226, 84, 25, 27, 125, 255, 166, 107, 217, 129, 34, 81, 225, 29, 255, 221, - 28, 18, 54, 218, 163, 165, 228, 169, 245, 69, 121, 73, 20, 147, 174, 32, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 7, 255, 255, - 255, 254, 239, 253, 240, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, - 255, 255, 255, 255, 255, 255, 255, 239, 255, 225, 32, 4, 170, 80, 33, 168, 204, 252, 192, 82, - 29, 40, 197, 195, 44, 25, 119, 27, 107, 81, 236, 115, 65, 156, 14, 227, 143, 157, 67, 206, 68, - 213, 151, 32, 3, 199, 127, 241, 39, 117, 107, 182, 129, 158, 168, 142, 66, 114, 44, 109, 129, - 131, 104, 138, 12, 38, 245, 98, 189, 157, 43, 138, 71, 185, 81, 116, 32, 3, 199, 127, 241, 39, - 117, 107, 182, 129, 158, 168, 142, 66, 114, 44, 109, 129, 131, 104, 138, 12, 38, 245, 98, 189, - 157, 43, 138, 71, 185, 81, 116, 32, 3, 199, 127, 241, 39, 117, 107, 182, 129, 158, 168, 142, - 66, 114, 44, 109, 129, 131, 104, 138, 12, 38, 245, 98, 189, 157, 43, 138, 71, 185, 81, 116, 32, - 3, 224, 113, 32, 203, 102, 54, 29, 74, 168, 32, 244, 72, 101, 142, 90, 218, 85, 146, 95, 207, - 205, 125, 30, 205, 251, 246, 244, 75, 157, 226, 227, 32, 3, 177, 144, 247, 243, 155, 40, 250, - 34, 169, 118, 21, 110, 116, 126, 106, 42, 128, 43, 110, 12, 254, 102, 47, 30, 131, 247, 45, - 226, 209, 209, 110, 32, 2, 188, 249, 94, 128, 100, 95, 41, 228, 82, 206, 13, 88, 95, 135, 180, - 4, 112, 219, 208, 164, 117, 98, 124, 4, 95, 105, 197, 126, 16, 129, 36, 32, 0, 31, 88, 35, 23, - 54, 31, 127, 12, 66, 185, 83, 136, 81, 26, 187, 47, 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