diff --git a/sway-lib-std/src/u128.sw b/sway-lib-std/src/u128.sw index 8eb22317b64..ef016cfe560 100644 --- a/sway-lib-std/src/u128.sw +++ b/sway-lib-std/src/u128.sw @@ -668,6 +668,17 @@ impl core::ops::Divide for U128 { } } +impl core::ops::Mod for U128 { + fn modulo(self, other: Self) -> Self { + assert(other != Self::zero()); + + // a mod b = a - b * (a / b) + let quotient = self / other; + let product = quotient * other; + self - product + } +} + fn u64_checked_add(a: u64, b: u64) -> Option { let of = asm(a: a, b: b, res) { add res a b; diff --git a/test/src/in_language_tests/test_programs/revert_inline_tests/src/main.sw b/test/src/in_language_tests/test_programs/revert_inline_tests/src/main.sw index 64c74e30b63..e11a6f413cd 100644 --- a/test/src/in_language_tests/test_programs/revert_inline_tests/src/main.sw +++ b/test/src/in_language_tests/test_programs/revert_inline_tests/src/main.sw @@ -18,4 +18,4 @@ fn pass_revert_require() { #[test(should_revert)] fn revert_revert_with_log() { revert_with_log("error") -} \ No newline at end of file +} diff --git a/test/src/in_language_tests/test_programs/u128_inline_tests/src/main.sw b/test/src/in_language_tests/test_programs/u128_inline_tests/src/main.sw index 4d7acda31fb..584a1716ad4 100644 --- a/test/src/in_language_tests/test_programs/u128_inline_tests/src/main.sw +++ b/test/src/in_language_tests/test_programs/u128_inline_tests/src/main.sw @@ -1,6 +1,14 @@ library; -use std::{u128::U128, registers::flags, flags::{set_flags, disable_panic_on_unsafe_math, disable_panic_on_overflow}}; +use std::{ + flags::{ + disable_panic_on_overflow, + disable_panic_on_unsafe_math, + set_flags, + }, + registers::flags, + u128::U128, +}; #[test] fn u128_from_u8() { @@ -686,6 +694,60 @@ fn u128_root() { assert(root_of_u_128 == U128::from((0, 1))); } +#[test] +fn u128_mod() { + let u128_zero = U128::zero(); + let u128_1 = U128::from((0, 1)); + let u128_2 = U128::from((0, 2)); + let u128_3 = U128::from((0, 3)); + let u128_max = U128::max(); + + assert(u128_zero % u128_1 == u128_zero); + assert(u128_zero % u128_2 == u128_zero); + assert(u128_zero % u128_3 == u128_zero); + assert(u128_zero % u128_max == u128_zero); + + assert(u128_1 % u128_1 == u128_zero); + assert(U128::from((0, 10)) % u128_1 == u128_zero); + assert(U128::from((0, 10000)) % u128_1 == u128_zero); + assert(u128_max % u128_1 == u128_zero); + + assert(u128_2 % u128_2 == u128_zero); + assert(u128_3 % u128_2 == u128_1); + assert(U128::from((0, 10)) % u128_2 == u128_zero); + assert(U128::from((0, 10000)) % u128_2 == u128_zero); + assert(U128::from((0, 10001)) % u128_2 == u128_1); + assert(U128::from((0, u64::max())) % u128_2 == u128_1); + assert(U128::from((u64::max(), 0)) % u128_2 == u128_zero); + assert(U128::from((u64::max(), 1)) % u128_2 == u128_1); + assert(u128_max % u128_2 == u128_1); + + assert(u128_3 % u128_3 == u128_zero); + assert(u128_2 % u128_3 == u128_2); + assert(u128_1 % u128_3 == u128_1); + assert(U128::from((0, 30000)) % u128_3 == u128_zero); + assert(U128::from((0, 30001)) % u128_3 == u128_1); + assert(U128::from((0, 30002)) % u128_3 == u128_2); + assert(U128::from((u64::max(), 0)) % u128_3 == u128_zero); + assert(U128::from((u64::max(), 1)) % u128_3 == u128_1); + assert(U128::from((u64::max(), 2)) % u128_3 == u128_2); + assert(u128_max % u128_3 == u128_zero); + + assert(U128::from((u64::max(), 0)) % U128::from((u64::max(), 0)) == u128_zero); + assert(U128::from((u64::max(), 1)) % U128::from((u64::max(), 0)) == u128_1); + assert(U128::from((u64::max(), 2)) % U128::from((u64::max(), 0)) == u128_2); + assert(U128::from((u64::max(), 3)) % U128::from((u64::max(), 0)) == u128_3); + assert(u128_max % U128::from((u64::max(), 0)) == U128::from((0, u64::max()))); +} + +#[test(should_revert)] +fn revert_u128_mod_zero() { + let a = U128::from((0, 1)); + let b = U128::zero(); + + let result = a % b; +} + #[test] fn u128_log() { let prior_flags = flags(); @@ -781,228 +843,272 @@ fn parity_u128_log_with_ruint() { // Failure cases found by comparing parity with ruint implementation of U128 // https://docs.rs/ruint/latest/src/ruint/log.rs.html#45-89 let a = [ - 2, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, - 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 15, 16, 16, 16, 16, 16, - 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, - 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, - 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, - 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, - 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, - 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, - 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, - 29, 29, 29, 29, 30, 30, 30, 30, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, - 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, - 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, - 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, - 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, - 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, - 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, - 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, - 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, - 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, - 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, - 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, - 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, - 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, - 42, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, - 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, - 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, - 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 47, 47, 47, 47, - 47, 47, 47, 47, 47, 47, 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, - 48, 48, 48, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, - 50, 50, 50, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 52, - 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, - 54, 54, 54, 54, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, - 56, 56, 56, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 60, 60, - 60, 60, 61, 61, 61, 62, 62, 63, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, - 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, - 64, 64, 64, 64, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, - 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, - 65, 65, 65, 65, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, - 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, - 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, - 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, - 67, 67, 67, 67, 67, 67, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, - 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, - 68, 68, 68, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, - 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 70, - 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, - 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 71, - 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, - 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, - 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, - 72, 72, 72, 72, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, - 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 74, 74, 74, 74, - 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, - 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, - 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, - 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, - 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, - 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, - 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, - 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, - 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 80, 80, 80, 80, - 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, - 80, 80, 80, 80, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, - 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, - 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 83, 83, 83, 83, 83, 83, 83, 83, - 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 84, 84, 84, 84, - 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 85, - 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, - 85, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, - 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, - 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, - 88, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 90, - 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 91, 91, 91, 91, - 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 92, 92, 92, 92, 92, 92, 92, 92, - 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, - 93, 93, 93, 93, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 95, 95, 95, - 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, - 96, 96, 96, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 98, 98, 98, 98, 98, 98, 98, - 98, 98, 98, 98, 98, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 100, 100, 100, 100, 100, - 100, 100, 100, 100, + 2, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, + 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, + 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, + 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, + 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, + 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, + 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, + 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, + 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, + 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29, + 29, 29, 30, 30, 30, 30, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, + 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, + 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, + 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, + 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, + 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, + 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, + 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, + 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, + 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, + 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, + 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, + 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, + 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, + 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, + 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, + 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, + 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, + 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, + 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, + 45, 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65, 65, + 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, + 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, + 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, + 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, + 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, + 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 68, + 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, + 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, + 68, 68, 68, 68, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, + 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, + 69, 69, 69, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, + 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, + 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 71, 71, 71, + 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, + 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72, 72, + 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, + 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 73, 73, 73, 73, 73, + 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, + 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 74, 74, 74, 74, 74, + 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, + 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 75, + 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, + 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, + 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, + 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, + 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, + 77, 77, 77, 77, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, + 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 79, + 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, + 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 80, 80, 80, 80, 80, 80, 80, + 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, + 80, 80, 80, 80, 80, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, + 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 82, 82, 82, 82, + 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, + 82, 82, 82, 82, 82, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, + 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 84, 84, 84, 84, 84, 84, + 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, + 84, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, + 85, 85, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, + 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, + 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, + 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, + 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, + 89, 89, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, + 90, 90, 90, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, + 91, 91, 91, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, + 92, 92, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, + 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 95, 95, 95, + 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 96, + 96, 96, 96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, + 97, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 99, 99, 99, 99, 99, 99, + 99, 99, 99, 99, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, ]; let b = [ - 3, 3, 5, 6, 7, 3, 6, 7, 3, 7, 3, 3, 9, 10, 11, 12, 13, 14, 15, 3, 10, 11, 12, 13, 14, 15, - 3, 11, 12, 13, 14, 15, 3, 12, 13, 14, 15, 3, 13, 14, 15, 3, 14, 15, 3, 15, 3, 3, 5, 6, 7, - 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 18, 19, 20, 21, 22, - 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, - 30, 31, 3, 5, 6, 7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 21, 22, 23, - 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, - 6, 7, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, - 6, 7, 25, 26, 27, 28, 29, 30, 31, 3, 6, 7, 26, 27, 28, 29, 30, 31, 3, 6, 7, 27, 28, 29, 30, - 31, 3, 6, 7, 28, 29, 30, 31, 3, 6, 7, 29, 30, 31, 3, 6, 7, 30, 31, 3, 6, 7, 31, 3, 6, 7, 3, - 6, 7, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, - 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 6, 7, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, - 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 6, 7, - 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, - 58, 59, 60, 61, 62, 63, 3, 6, 7, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, - 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 37, 38, 39, 40, 41, 42, 43, - 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 38, - 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, - 62, 63, 3, 7, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, - 58, 59, 60, 61, 62, 63, 3, 7, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, - 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, - 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, - 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 43, 44, 45, 46, 47, 48, 49, 50, 51, - 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 44, 45, 46, 47, 48, 49, 50, 51, 52, - 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, - 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, - 58, 59, 60, 61, 62, 63, 3, 7, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, - 62, 63, 3, 7, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 49, 50, - 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 50, 51, 52, 53, 54, 55, 56, 57, 58, - 59, 60, 61, 62, 63, 3, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 52, 53, 54, - 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 54, - 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 56, 57, 58, - 59, 60, 61, 62, 63, 3, 57, 58, 59, 60, 61, 62, 63, 3, 58, 59, 60, 61, 62, 63, 3, 59, 60, - 61, 62, 63, 3, 60, 61, 62, 63, 3, 61, 62, 63, 3, 62, 63, 3, 63, 3, 3, 5, 6, 7, 9, 10, 11, - 12, 13, 14, 15, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, - 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, - 12, 13, 14, 15, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, - 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, - 13, 14, 15, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, - 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, - 15, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, - 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 69, 70, - 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, - 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 70, 71, 72, 73, 74, 75, - 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, - 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, - 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, - 10, 11, 12, 13, 14, 15, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, - 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 73, - 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, - 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 74, 75, 76, 77, 78, 79, 80, 81, 82, - 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, - 11, 12, 13, 14, 15, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, - 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 76, 77, 78, 79, 80, - 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, - 7, 9, 10, 11, 12, 13, 14, 15, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, - 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 78, 79, 80, 81, - 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, - 10, 11, 12, 13, 14, 15, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, - 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 80, 81, 82, 83, 84, 85, 86, 87, - 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, - 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, - 7, 10, 11, 12, 13, 14, 15, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, - 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, - 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 84, 85, 86, 87, 88, - 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 85, - 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, - 14, 15, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, - 12, 13, 14, 15, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, - 11, 12, 13, 14, 15, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, - 11, 12, 13, 14, 15, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, - 12, 13, 14, 15, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, - 14, 15, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 92, - 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 93, 94, 95, 96, 97, - 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, - 10, 11, 12, 13, 14, 15, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 96, - 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, - 12, 13, 14, 15, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 99, 100, 3, 5, 6, 7, 10, - 11, 12, 13, 14, 15, 100, 3, 5, 6, 7, 11, 12, 13, 14, 15, + 3, 3, 5, 6, 7, 3, 6, 7, 3, 7, 3, 3, 9, 10, 11, 12, 13, 14, 15, 3, 10, 11, + 12, 13, 14, 15, 3, 11, 12, 13, 14, 15, 3, 12, 13, 14, 15, 3, 13, 14, 15, 3, + 14, 15, 3, 15, 3, 3, 5, 6, 7, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, + 28, 29, 30, 31, 3, 5, 6, 7, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, + 30, 31, 3, 5, 6, 7, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, + 5, 6, 7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 21, 22, + 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 22, 23, 24, 25, 26, 27, 28, + 29, 30, 31, 3, 5, 6, 7, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 24, + 25, 26, 27, 28, 29, 30, 31, 3, 5, 6, 7, 25, 26, 27, 28, 29, 30, 31, 3, 6, + 7, 26, 27, 28, 29, 30, 31, 3, 6, 7, 27, 28, 29, 30, 31, 3, 6, 7, 28, 29, 30, + 31, 3, 6, 7, 29, 30, 31, 3, 6, 7, 30, 31, 3, 6, 7, 31, 3, 6, 7, 3, 6, 7, 33, + 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, + 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 6, 7, 34, 35, 36, 37, 38, 39, + 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, + 59, 60, 61, 62, 63, 3, 6, 7, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, + 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 6, + 7, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, + 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 37, 38, 39, 40, 41, 42, 43, + 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, + 63, 3, 7, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, + 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 39, 40, 41, 42, 43, 44, 45, + 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, + 7, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, + 58, 59, 60, 61, 62, 63, 3, 7, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, + 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 42, 43, 44, 45, 46, + 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, + 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, + 62, 63, 3, 7, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, + 59, 60, 61, 62, 63, 3, 7, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, + 57, 58, 59, 60, 61, 62, 63, 3, 7, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, + 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 47, 48, 49, 50, 51, 52, 53, 54, 55, + 56, 57, 58, 59, 60, 61, 62, 63, 3, 7, 48, 49, 50, 51, 52, 53, 54, 55, 56, + 57, 58, 59, 60, 61, 62, 63, 3, 7, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, + 59, 60, 61, 62, 63, 3, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, + 63, 3, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 52, 53, 54, + 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 53, 54, 55, 56, 57, 58, 59, 60, 61, + 62, 63, 3, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 3, 55, 56, 57, 58, 59, + 60, 61, 62, 63, 3, 56, 57, 58, 59, 60, 61, 62, 63, 3, 57, 58, 59, 60, 61, + 62, 63, 3, 58, 59, 60, 61, 62, 63, 3, 59, 60, 61, 62, 63, 3, 60, 61, 62, 63, + 3, 61, 62, 63, 3, 62, 63, 3, 63, 3, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, + 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, + 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, + 6, 7, 9, 10, 11, 12, 13, 14, 15, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, + 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, + 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 67, 68, 69, 70, + 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, + 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, + 14, 15, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, + 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, + 7, 9, 10, 11, 12, 13, 14, 15, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, + 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, + 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 70, 71, 72, 73, 74, 75, 76, + 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, + 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 71, 72, 73, 74, + 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, + 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 72, 73, + 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, + 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 73, + 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, + 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 74, + 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, + 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 75, 76, + 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, + 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 76, 77, 78, 79, + 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, + 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 77, 78, 79, 80, 81, 82, 83, + 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, + 6, 7, 9, 10, 11, 12, 13, 14, 15, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, + 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, + 13, 14, 15, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, + 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 80, 81, 82, + 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, + 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, + 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, + 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, + 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, + 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 84, 85, + 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, + 11, 12, 13, 14, 15, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, + 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 86, 87, 88, 89, 90, 91, 92, 93, + 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 87, 88, 89, + 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, + 15, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, + 12, 13, 14, 15, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, + 7, 10, 11, 12, 13, 14, 15, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, + 5, 6, 7, 10, 11, 12, 13, 14, 15, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, + 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 92, 93, 94, 95, 96, 97, 98, 99, 100, 3, + 5, 6, 7, 10, 11, 12, 13, 14, 15, 93, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, + 7, 10, 11, 12, 13, 14, 15, 94, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, + 12, 13, 14, 15, 95, 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, + 96, 97, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 97, 98, 99, 100, + 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 98, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, + 14, 15, 99, 100, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 100, 3, 5, 6, 7, 11, + 12, 13, 14, 15, ]; let expected = [ - 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, - 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, - 0, 0, 0, 0, 0, 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