finitedomain
Version:
A fast feature rich finite domain solver
153 lines (125 loc) • 231 kB
JavaScript
import expect from '../fixtures/mocha_proxy.fixt';
import {
fixt_assertStrings,
fixt_dom_empty,
fixt_dom_nums,
fixt_dom_range,
fixt_dom_ranges,
fixt_dom_solved,
fixt_domainEql,
fixt_strdom_empty,
} from '../fixtures/domain.fixt';
import {
SUP,
} from '../../src/helpers';
import {
domain__debug,
} from '../../src/domain';
import domain_plus from '../../src/doms/domain_plus';
describe('src/plus.spec.js', function() {
this.timeout(60000); // takes long under istanbul / even longer under travis
describe('domain_plus unit tests', function() {
it('should exist', function() {
expect(domain_plus).to.be.a('function');
});
it('should require domains', function() {
expect(() => domain_plus()).to.throw('ONLY_NORDOM');
expect(() => domain_plus(fixt_dom_empty())).to.throw('ONLY_NORDOM');
expect(() => domain_plus(null, fixt_dom_empty())).to.throw('ONLY_NORDOM');
});
it('should accept empty domains', function() {
expect(domain_plus(fixt_dom_empty(), fixt_dom_empty())).to.eql(fixt_dom_empty());
});
it('should throw for empty strdoms', function() {
expect(_ => domain_plus(fixt_strdom_empty(), fixt_dom_empty())).to.throw('empty domains are always numdoms');
expect(_ => domain_plus(fixt_dom_empty(), fixt_strdom_empty())).to.throw('empty domains are always numdoms');
expect(_ => domain_plus(fixt_strdom_empty(), fixt_strdom_empty())).to.throw('empty domains are always numdoms');
});
describe('with array', function() {
it('should add two ranges', function() {
let A = fixt_dom_range(5, 10);
let B = fixt_dom_range(50, 60);
let E = fixt_dom_range(55, 70);
fixt_assertStrings(domain_plus(A, B), E);
});
it('should add two domains', function() {
let A = fixt_dom_ranges([5, 10], [20, 35]);
let B = fixt_dom_ranges([50, 60], [110, 128]);
let E = fixt_dom_ranges([55, 95], [115, 163]);
fixt_assertStrings(domain_plus(A, B), E);
});
it('should add two domains', function() {
let A = fixt_dom_ranges([0, 1], [4, 12], [15, 17], [100, 100]);
let B = fixt_dom_ranges([0, 1], [4, 12], [15, 17], [100, 100]);
let E = fixt_dom_ranges([0, 2], [4, 34], [100, 101], [104, 112], [115, 117], [200, 200]);
fixt_assertStrings(domain_plus(A, B), E);
});
it('should not exceed SUP (SUP+1)', function() {
// since [SUP, SUP] + [1, 1] would be [SUP+1, SUP+1] the result is OOB and empty
// let's hope this never really hurts us irl... but we must have this protection
// or it may introduce inconsistent domains into the internals, which is bad.
let A = fixt_dom_solved(SUP);
let B = fixt_dom_solved(1);
let E = fixt_dom_empty();
expect(domain_plus(A, B)).to.eql(E);
});
it('should not exceed SUP (1+SUP)', function() {
// since [1, 1] + [SUP, SUP] would be [SUP+1, SUP+1] the result is OOB and empty
// let's hope this never really hurts us irl... but we must have this protection
// or it may introduce inconsistent domains into the internals, which is bad.
let A = fixt_dom_solved(1);
let B = fixt_dom_solved(SUP);
let E = fixt_dom_empty();
expect(domain_plus(A, B)).to.eql(E);
});
});
describe('with numbers', function() {
it('should add two ranges', function() {
let A = fixt_dom_range(5, 10);
let B = fixt_dom_range(50, 60);
let E = fixt_dom_range(55, 70);
fixt_assertStrings(domain_plus(A, B), E);
});
it('should add two domains (1)', function() {
let A = fixt_dom_ranges([5, 10], [20, 35]);
let B = fixt_dom_ranges([50, 60], [110, 128]);
let E = fixt_dom_ranges([55, 95], [115, 163]);
fixt_assertStrings(domain_plus(A, B), E);
});
it('should add two domains (2)', function() {
let A = fixt_dom_ranges([0, 1], [4, 12], [15, 17]);
let B = fixt_dom_ranges([0, 1], [4, 12], [15, 17]);
let E = fixt_dom_ranges([0, 2], [4, 34]);
fixt_assertStrings(domain_plus(A, B), E);
});
it('should add small numbers to a small domain', function() {
// regression. numbers 0 ~ 3 are hardcoded explicitly, 4+ is loop
// make sure total does not exceed the small domain cap
for (let i = 0; i < 7; ++i) {
for (let j = 0; j < 8; ++j) {
if (i !== 8 || j !== 8) { // 16
expect(domain_plus(1 << i, 1 << j), i + ' + ' + j).to.eql(1 << (i + j));
}
}
}
});
});
});
describe('red herrings', function() {
describe('small domains', function() {
let inputs = [
// randomly generated
134258832, 1141243913, 277057, 807420480, 29696008, 134357520, 50351424, 1275596820, 54525952, 537997320,
18891266, 281018896, 144715916, 40517721, 37290240, 37879816, 134514689, 1648492544, 78118912, 3171072,
685277253, 1476608577, 16391, 655508, 1073807616,
// all permutations of the first 5 bits
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
// only one bit set for all bits
1 << 0, 1 << 1, 1 << 2, 1 << 3, 1 << 4, 1 << 5, 1 << 6, 1 << 7, 1 << 8, 1 << 9, 1 << 10, 1 << 11, 1 << 12, 1 << 13, 1 << 14, 1 << 15, 1 << 16,
1 << 17, 1 << 18, 1 << 19, 1 << 20, 1 << 21, 1 << 22, 1 << 23, 1 << 24, 1 << 25, 1 << 26, 1 << 27, 1 << 28, 1 << 29, 1 << 30,
];
//console.log(inputs.map(a=>inputs.map(b=>JSON.stringify(domain_plus(a, b)).replace(/"/g, ''))).join(', '))
// these are the outcomes when crossing each input with each other input (or itself), ordered.
// they were generated from a more rigid version of the code. they serve as canaries.
let outcomes = [
[8, 8, 11, 11, 14, 14, 17, 17, 19, 20, 22, 22, 26, 26, 28, 28, 30, 31, 34, 34, 40, 40, 42, 42, 54, 54], [4, 4, 7, 7, 10, 10, 13, 13, 15, 16, 18, 18, 21, 22, 24, 25, 27, 27, 30, 34, 37, 37, 39, 39, 41, 41, 43, 45, 53, 53, 57, 57], [4, 4, 7, 7, 10, 10, 13, 13, 15, 22, 24, 28, 31, 31, 33, 33, 36, 36, 38, 40, 45, 45], [10, 10, 13, 13, 16, 16, 18, 19, 21, 22, 24, 25, 27, 29, 32, 36, 41, 44, 48, 48, 55, 56], [7, 7, 10, 10, 16, 18, 20, 20, 22, 23, 25, 31, 33, 33, 35, 40, 43, 43, 45, 45, 49, 51], [8, 8, 11, 11, 13, 13, 16, 17, 19, 22, 24, 24, 26, 26, 28, 28, 30, 32, 34, 34, 36, 36, 40, 40, 42, 42, 44, 44, 54, 54], [10, 10, 12, 15, 17, 19, 21, 21, 23, 29, 31, 33, 35, 35, 37, 41, 51, 52], [6, 6, 8, 9, 11, 11, 15, 17, 19, 19, 23, 23, 25, 27, 29, 34, 37, 37, 39, 43, 45, 46, 53, 54, 57, 57], [26, 26, 28, 29, 31, 32, 35, 35, 37, 40, 49, 49, 51, 52], [7, 7, 10, 10, 16, 20, 23, 31, 33, 33, 35, 36, 39, 40, 42, 44, 47, 47, 56, 56], [5, 5, 8, 8, 13, 14, 16, 16, 18, 18, 21, 22, 24, 25, 27, 29, 31, 31, 34, 34, 36, 37, 39, 39, 41, 41, 48, 48, 51, 51], [8, 8, 11, 11, 13, 13, 16, 17, 19, 19, 22, 22, 24, 24, 26, 27, 29, 32, 35, 38, 41, 41, 43, 43, 49, 50, 55, 55], [6, 7, 9, 11, 14, 20, 22, 22, 25, 31, 34, 34, 36, 36, 38, 40, 42, 42, 48, 48, 50, 50, 54, 54], [4, 4, 7, 8, 10, 11, 13, 13, 15, 19, 21, 21, 23, 38, 40, 41, 44, 44, 46, 46, 48, 49, 52, 52], [12, 12, 15, 15, 20, 21, 23, 29, 31, 36, 38, 38, 40, 40, 43, 43, 46, 48, 52, 52], [7, 7, 10, 10, 16, 16, 18, 18, 21, 21, 24, 24, 26, 26, 29, 30, 32, 32, 35, 35, 37, 38, 40, 40, 44, 44, 49, 49, 52, 52], [4, 4, 7, 7, 13, 13, 15, 15, 18, 19, 22, 22, 24, 28, 30, 31, 33, 34, 38, 38, 40, 40, 42, 42, 45, 45, 54, 54], [21, 21, 24, 24, 26, 26, 29, 30, 32, 38, 40, 40, 42, 45, 49, 49, 52, 52, 56, 57], [23, 23, 25, 28, 30, 30, 32, 34, 36, 36, 38, 39, 41, 41, 46, 46, 48, 48, 50, 50, 53, 53], [12, 13, 15, 18, 20, 29, 33, 36, 40, 41, 47, 48], [4, 4, 6, 7, 9, 10, 13, 13, 15, 15, 17, 17, 19, 19, 21, 24, 26, 38, 40, 40, 42, 42, 44, 44, 46, 47, 49, 50, 54, 54, 56, 56], [4, 4, 7, 7, 10, 10, 13, 13, 15, 16, 18, 24, 27, 27, 29, 37, 40, 45, 54, 55, 57, 57], [4, 9, 13, 18, 21, 21, 27, 29, 41, 41], [6, 6, 8, 9, 11, 11, 14, 15, 17, 17, 19, 24, 26, 26, 29, 32, 34, 34, 44, 44, 46, 46], [12, 12, 15, 15, 20, 21, 23, 23, 29, 29, 31, 31, 34, 35, 37, 37, 43, 43, 45, 45, 57, 57], 134258832, 268517664, 402776496, 537035328, 671261392, 805552992, 939779056, 1074070656, 1208329360, 1342522784, 1476781488, 1611105984, 1745331920, 1879558112, 2013784048, [8, 8, 11, 11, 17, 17, 19, 19, 31, 31], [4, 4, 7, 8, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 27, 27, 31, 31], [5, 5, 8, 8, 11, 11, 14, 14, 16, 17, 19, 19, 28, 28, 31, 31], [4, 5, 7, 8, 11, 11, 13, 17, 19, 19, 27, 28, 31, 31], [6, 6, 8, 9, 11, 11, 15, 15, 17, 17, 19, 19, 29, 29, 31, 31], [4, 4, 6, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 27, 27, 29, 29, 31, 31], [5, 6, 8, 9, 11, 11, 14, 17, 19, 19, 28, 29, 31, 31], [4, 9, 11, 11, 13, 17, 19, 19, 27, 29, 31, 31], [7, 8, 10, 11, 16, 19, 30, 31], [4, 4, 7, 8, 10, 11, 13, 13, 15, 19, 27, 27, 30, 31], [5, 5, 7, 8, 10, 11, 14, 14, 16, 19, 28, 28, 30, 31], [4, 5, 7, 8, 10, 11, 13, 19, 27, 28, 30, 31], [6, 11, 15, 19, 29, 31], [4, 4, 6, 11, 13, 13, 15, 19, 27, 27, 29, 31], [5, 11, 14, 19, 28, 31], [4, 11, 13, 19, 27, 31], 134258832, 268517664, 537035328, 1074070656, [8, 8, 11, 11, 17, 17, 19, 19, 31, 31], [9, 9, 12, 12, 18, 18, 20, 20, 32, 32], [10, 10, 13, 13, 19, 19, 21, 21, 33, 33], [11, 11, 14, 14, 20, 20, 22, 22, 34, 34], [12, 12, 15, 15, 21, 21, 23, 23, 35, 35], [13, 13, 16, 16, 22, 22, 24, 24, 36, 36], [14, 14, 17, 17, 23, 23, 25, 25, 37, 37], [15, 15, 18, 18, 24, 24, 26, 26, 38, 38], [16, 16, 19, 19, 25, 25, 27, 27, 39, 39], [17, 17, 20, 20, 26, 26, 28, 28, 40, 40], [18, 18, 21, 21, 27, 27, 29, 29, 41, 41], [19, 19, 22, 22, 28, 28, 30, 30, 42, 42], [20, 20, 23, 23, 29, 29, 31, 31, 43, 43], [21, 21, 24, 24, 30, 30, 32, 32, 44, 44], [22, 22, 25, 25, 31, 31, 33, 33, 45, 45], [23, 23, 26, 26, 32, 32, 34, 34, 46, 46], [24, 24, 27, 27, 33, 33, 35, 35, 47, 47], [25, 25, 28, 28, 34, 34, 36, 36, 48, 48], [26, 26, 29, 29, 35, 35, 37, 37, 49, 49], [27, 27, 30, 30, 36, 36, 38, 38, 50, 50], [28, 28, 31, 31, 37, 37, 39, 39, 51, 51], [29, 29, 32, 32, 38, 38, 40, 40, 52, 52], [30, 30, 33, 33, 39, 39, 41, 41, 53, 53], [31, 31, 34, 34, 40, 40, 42, 42, 54, 54], [32, 32, 35, 35, 41, 41, 43, 43, 55, 55], [33, 33, 36, 36, 42, 42, 44, 44, 56, 56], [34, 34, 37, 37, 43, 43, 45, 45, 57, 57], [4, 4, 7, 7, 10, 10, 13, 13, 15, 16, 18, 18, 21, 22, 24, 25, 27, 27, 30, 34, 37, 37, 39, 39, 41, 41, 43, 45, 53, 53, 57, 57], [0, 0, 3, 3, 6, 6, 17, 18, 20, 21, 26, 26, 29, 30, 33, 36, 43, 44, 47, 48, 52, 52, 56, 56, 60, 60], [0, 0, 3, 3, 6, 6, 9, 9, 11, 18, 21, 21, 23, 24, 26, 32, 35, 39, 41, 44, 48, 48], [6, 6, 9, 9, 12, 12, 14, 14, 17, 17, 21, 21, 23, 24, 26, 29, 31, 32, 35, 36, 38, 40, 44, 47, 51, 51, 54, 55, 58, 59], [3, 3, 6, 6, 13, 13, 16, 16, 18, 27, 29, 31, 33, 36, 39, 44, 46, 46, 48, 50, 52, 54], [4, 4, 7, 7, 9, 9, 12, 13, 16, 17, 20, 22, 26, 27, 30, 31, 34, 35, 39, 39, 43, 45, 47, 47, 53, 53, 57, 57], [6, 6, 8, 11, 13, 14, 17, 17, 23, 29, 31, 32, 34, 34, 36, 38, 40, 44, 50, 51, 54, 55], [2, 2, 4, 5, 7, 7, 12, 12, 15, 15, 19, 22, 26, 30, 32, 34, 36, 38, 42, 45, 47, 49, 52, 53, 56, 57, 60, 60], [22, 22, 24, 25, 27, 28, 39, 43, 48, 48, 50, 52, 54, 55], [3, 3, 6, 6, 12, 13, 15, 16, 19, 21, 23, 23, 29, 34, 37, 39, 42, 43, 46, 47, 50, 50, 55, 55, 59, 59], [1, 1, 4, 4, 9, 9, 12, 12, 14, 14, 17, 19, 21, 21, 24, 24, 26, 27, 31, 32, 35, 35, 38, 42, 44, 44, 47, 47, 50, 51, 54, 54], [4, 4, 7, 7, 9, 9, 12, 12, 21, 23, 25, 28, 30, 31, 34, 35, 39, 41, 45, 46, 48, 49, 52, 54, 58, 58], [2, 3, 5, 7, 10, 10, 12, 13, 15, 16, 19, 21, 23, 33, 37, 45, 47, 47, 49, 49, 51, 51, 53, 53, 57, 57], [0, 0, 3, 4, 6, 7, 9, 9, 14, 14, 17, 26, 28, 40, 42, 45, 47, 49, 51, 52, 55, 55], [8, 8, 11, 11, 16, 16, 19, 26, 28, 28, 33, 34, 36, 39, 42, 43, 45, 47, 49, 51, 55, 55], [3, 3, 6, 6, 17, 17, 20, 22, 25, 25, 28, 29, 33, 35, 39, 40, 42, 43, 47, 48, 51, 52, 55, 55], [0, 0, 3, 3, 11, 11, 14, 15, 17, 18, 21, 21, 26, 30, 32, 33, 35, 37, 41, 41, 44, 45, 48, 48, 53, 53, 57, 57], [17, 17, 20, 20, 22, 22, 25, 25, 28, 30, 32, 35, 39, 40, 42, 43, 46, 48, 51, 52, 55, 56, 59, 60], [19, 19, 21, 24, 26, 26, 29, 29, 36, 41, 43, 45, 47, 47, 49, 49, 51, 53, 56, 56], [8, 9, 11, 14, 16, 17, 20, 21, 23, 27, 30, 32, 34, 35, 37, 40, 43, 44, 46, 47, 50, 51], [0, 0, 2, 3, 5, 6, 9, 9, 15, 15, 17, 20, 22, 30, 32, 33, 36, 41, 44, 50, 52, 53, 55, 55, 57, 57, 59, 59], [0, 0, 3, 3, 6, 6, 9, 9, 12, 12, 14, 14, 16, 20, 23, 24, 26, 28, 30, 36, 39, 40, 42, 48, 53, 54, 56, 58, 60, 60], [0, 5, 14, 14, 17, 20, 26, 28, 30, 32, 40, 40, 44, 44], [2, 2, 4, 5, 7, 7, 10, 10, 17, 17, 19, 22, 24, 25, 28, 28, 30, 30, 32, 37, 43, 43, 45, 45, 47, 47, 49, 49], [8, 8, 11, 11, 16, 16, 19, 19, 25, 26, 30, 30, 33, 34, 38, 38, 42, 42, 46, 48, 56, 56, 60, 60], 1141243913, [1, 1, 4, 4, 18, 19, 27, 27, 31, 31], [0, 1, 3, 4, 17, 19, 26, 27, 30, 31], [2, 2, 5, 5, 19, 20, 28, 28, 32, 32], [0, 0, 2, 3, 5, 5, 17, 20, 26, 26, 28, 28, 30, 30, 32, 32], [1, 2, 4, 5, 18, 20, 27, 28, 31, 32], [0, 5, 17, 20, 26, 28, 30, 32], [3, 3, 6, 6, 20, 21, 29, 29, 33, 33], [0, 0, 3, 3, 6, 6, 17, 18, 20, 21, 26, 26, 29, 30, 33, 33], [1, 1, 3, 4, 6, 6, 18, 21, 27, 27, 29, 29, 31, 31, 33, 33], [0, 1, 3, 4, 6, 6, 17, 21, 26, 27, 29, 31, 33, 33], [2, 3, 5, 6, 19, 21, 28, 29, 32, 33], [0, 0, 2, 3, 5, 6, 17, 21, 26, 26, 28, 30, 32, 33], [1, 6, 18, 21, 27, 29, 31, 33], [0, 6, 17, 21, 26, 33], [4, 4, 7, 7, 21, 22, 30, 30, 34, 34], [0, 0, 3, 4, 7, 7, 17, 18, 21, 22, 26, 26, 30, 30, 34, 34], [1, 1, 4, 4, 7, 7, 18, 19, 21, 22, 27, 27, 30, 31, 34, 34], [0, 1, 3, 4, 7, 7, 17, 19, 21, 22, 26, 27, 30, 31, 34, 34], [2, 2, 4, 5, 7, 7, 19, 22, 28, 28, 30, 30, 32, 32, 34, 34], [0, 0, 2, 5, 7, 7, 17, 22, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34], [1, 2, 4, 5, 7, 7, 18, 22, 27, 28, 30, 32, 34, 34], [0, 5, 7, 7, 17, 22, 26, 28, 30, 32, 34, 34], [3, 4, 6, 7, 20, 22, 29, 30, 33, 34], [0, 0, 3, 4, 6, 7, 17, 18, 20, 22, 26, 26, 29, 30, 33, 34], [1, 1, 3, 4, 6, 7, 18, 22, 27, 27, 29, 31, 33, 34], [0, 1, 3, 4, 6, 7, 17, 22, 26, 27, 29, 31, 33, 34], [2, 7, 19, 22, 28, 30, 32, 34], [0, 0, 2, 7, 17, 22, 26, 26, 28, 30, 32, 34], [1, 7, 18, 22, 27, 34], [0, 7, 17, 22, 26, 34], 1141243913, [1, 1, 4, 4, 18, 19, 27, 27, 31, 31], [2, 2, 5, 5, 19, 20, 28, 28, 32, 32], [3, 3, 6, 6, 20, 21, 29, 29, 33, 33], [4, 4, 7, 7, 21, 22, 30, 30, 34, 34], [5, 5, 8, 8, 22, 23, 31, 31, 35, 35], [6, 6, 9, 9, 23, 24, 32, 32, 36, 36], [7, 7, 10, 10, 24, 25, 33, 33, 37, 37], [8, 8, 11, 11, 25, 26, 34, 34, 38, 38], [9, 9, 12, 12, 26, 27, 35, 35, 39, 39], [10, 10, 13, 13, 27, 28, 36, 36, 40, 40], [11, 11, 14, 14, 28, 29, 37, 37, 41, 41], [12, 12, 15, 15, 29, 30, 38, 38, 42, 42], [13, 13, 16, 16, 30, 31, 39, 39, 43, 43], [14, 14, 17, 17, 31, 32, 40, 40, 44, 44], [15, 15, 18, 18, 32, 33, 41, 41, 45, 45], [16, 16, 19, 19, 33, 34, 42, 42, 46, 46], [17, 17, 20, 20, 34, 35, 43, 43, 47, 47], [18, 18, 21, 21, 35, 36, 44, 44, 48, 48], [19, 19, 22, 22, 36, 37, 45, 45, 49, 49], [20, 20, 23, 23, 37, 38, 46, 46, 50, 50], [21, 21, 24, 24, 38, 39, 47, 47, 51, 51], [22, 22, 25, 25, 39, 40, 48, 48, 52, 52], [23, 23, 26, 26, 40, 41, 49, 49, 53, 53], [24, 24, 27, 27, 41, 42, 50, 50, 54, 54], [25, 25, 28, 28, 42, 43, 51, 51, 55, 55], [26, 26, 29, 29, 43, 44, 52, 52, 56, 56], [27, 27, 30, 30, 44, 45, 53, 53, 57, 57], [28, 28, 31, 31, 45, 46, 54, 54, 58, 58], [29, 29, 32, 32, 46, 47, 55, 55, 59, 59], [30, 30, 33, 33, 47, 48, 56, 56, 60, 60], [4, 4, 7, 7, 10, 10, 13, 13, 15, 22, 24, 28, 31, 31, 33, 33, 36, 36, 38, 40, 45, 45], [0, 0, 3, 3, 6, 6, 9, 9, 11, 18, 21, 21, 23, 24, 26, 32, 35, 39, 41, 44, 48, 48], [0, 0, 6, 6, 9, 9, 11, 13, 15, 15, 17, 27, 29, 31, 36, 36], [6, 6, 9, 9, 12, 12, 14, 15, 17, 30, 32, 35, 37, 42, 46, 47], [3, 3, 9, 9, 12, 16, 18, 19, 21, 37, 40, 42], [4, 4, 9, 10, 13, 13, 15, 31, 33, 33, 35, 36, 38, 40, 45, 45], [6, 6, 8, 8, 10, 12, 14, 38, 42, 43], [2, 2, 4, 4, 8, 8, 10, 28, 30, 33, 35, 45, 48, 48], [22, 22, 24, 25, 28, 28, 30, 31, 33, 38, 40, 40, 42, 43], [3, 3, 9, 9, 12, 16, 18, 35, 38, 38, 40, 42, 47, 47], [1, 1, 7, 7, 9, 10, 12, 15, 18, 27, 30, 30, 32, 37, 39, 39, 42, 42], [4, 4, 9, 10, 13, 13, 15, 18, 20, 23, 27, 29, 31, 37, 39, 41, 46, 46], [2, 3, 7, 9, 11, 16, 18, 27, 29, 36, 38, 41, 45, 45], [0, 0, 3, 4, 6, 6, 9, 40, 43, 43], [8, 8, 14, 14, 16, 17, 19, 22, 25, 34, 36, 39, 43, 43], [3, 3, 9, 9, 12, 12, 14, 17, 21, 23, 25, 26, 28, 31, 33, 38, 40, 40, 43, 43], [0, 0, 6, 6, 9, 9, 11, 13, 15, 15, 17, 18, 20, 24, 26, 31, 33, 33, 36, 36, 38, 40, 45, 45], [17, 17, 22, 23, 25, 26, 28, 31, 33, 43, 47, 48], [19, 19, 21, 21, 23, 23, 25, 39, 41, 41, 44, 44], [8, 9, 13, 15, 17, 27, 29, 34, 38, 39], [0, 0, 2, 2, 6, 6, 8, 9, 11, 15, 17, 42, 45, 45, 47, 47], [0, 0, 6, 6, 9, 9, 11, 30, 32, 43, 45, 46, 48, 48], [0, 2, 6, 15, 18, 20, 23, 23, 25, 27, 32, 32], [2, 2, 4, 4, 7, 8, 10, 11, 13, 20, 22, 23, 25, 26, 28, 32, 35, 35, 37, 37], [8, 8, 14, 14, 16, 17, 19, 22, 25, 30, 34, 34, 36, 36, 39, 39, 41, 43, 48, 48], 277057, 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