Farey successor sequence: terminal equality · case 01

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x
    a,b,c,d=0,1,1,n
    out=[[0,1]]
    for _ in range(500):
     if c>n: break
     out.append([c,d])
     if d<=0: return None
     k=(n+b)//d
     a,b,c,d=c,d,k*c-a,k*d-b
     if a==b-1: break
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(2, [[0, 1], [1, 2], [1, 1]]), (1, [[0, 1], [1, 1]]), (24, [[0, 1], [1, 24], [1, 23], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [2, 23], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [3, 23], [2, 15], [3, 22], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [4, 23], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [5, 24], [4, 19], [3, 14], [5, 23], [2, 9], [5, 22], [3, 13], [4, 17], [5, 21], [1, 4], [6, 23], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [7, 24], [5, 17], [3, 10], [7, 23], [4, 13], [5, 16], [6, 19], [7, 22], [1, 3], [8, 23], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [9, 23], [2, 5], [9, 22], [7, 17], [5, 12], [8, 19], [3, 7], [10, 23], [7, 16], [4, 9], [9, 20], [5, 11], [11, 24], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [11, 23], [1, 2], [12, 23], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [13, 24], [6, 11], [11, 20], [5, 9], [9, 16], [13, 23], [4, 7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [14, 23], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [15, 23], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [16, 23], [7, 10], [12, 17], [17, 24], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [19, 24], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [1, 1]]), (3, [[0, 1], [1, 3], [1, 2], [2, 3], [1, 1]]), (4, [[0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]]), (5, [[0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3], [3, 4], [4, 5], [1, 1]]), (6, [[0, 1], [1, 6], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3], [3, 4], [4, 5], [5, 6], [1, 1]]), (7, [[0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [2, 5], [3, 7], [1, 2], [4, 7], [3, 5], [2, 3], [5, 7], [3, 4], [4, 5], [5, 6], [6, 7], [1, 1]])], [(3, [[0, 1], [1, 3], [1, 2], [2, 3], [1, 1]]), (5, [[0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3], [3, 4], [4, 5], [1, 1]]), (1, [[0, 1], [1, 1]]), (24, [[0, 1], [1, 24], [1, 23], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [2, 23], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [3, 23], [2, 15], [3, 22], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [4, 23], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [5, 24], [4, 19], [3, 14], [5, 23], [2, 9], [5, 22], [3, 13], [4, 17], [5, 21], [1, 4], [6, 23], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [7, 24], [5, 17], [3, 10], [7, 23], [4, 13], [5, 16], [6, 19], [7, 22], [1, 3], [8, 23], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [9, 23], [2, 5], [9, 22], [7, 17], [5, 12], [8, 19], [3, 7], [10, 23], [7, 16], [4, 9], [9, 20], [5, 11], [11, 24], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [11, 23], [1, 2], [12, 23], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [13, 24], [6, 11], [11, 20], [5, 9], [9, 16], [13, 23], [4, 7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [14, 23], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [15, 23], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [16, 23], [7, 10], [12, 17], [17, 24], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [19, 24], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [1, 1]]), (18, [[0, 1], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [1, 11], [1, 10], [1, 9], [2, 17], [1, 8], [2, 15], [1, 7], [2, 13], [1, 6], [3, 17], [2, 11], [3, 16], [1, 5], [3, 14], [2, 9], [3, 13], [4, 17], [1, 4], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [4, 13], [5, 16], [1, 3], [6, 17], [5, 14], [4, 11], [3, 8], [5, 13], [7, 18], [2, 5], [7, 17], [5, 12], [3, 7], [7, 16], [4, 9], [5, 11], [6, 13], [7, 15], [8, 17], [1, 2], [9, 17], [8, 15], [7, 13], [6, 11], [5, 9], [9, 16], [4, 7], [7, 12], [10, 17], [3, 5], [11, 18], [8, 13], [5, 8], [7, 11], [9, 14], [11, 17], [2, 3], [11, 16], [9, 13], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [3, 4], [13, 17], [10, 13], [7, 9], [11, 14], [4, 5], [13, 16], [9, 11], [14, 17], [5, 6], [11, 13], [6, 7], [13, 15], [7, 8], [15, 17], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [1, 1]]), (19, [[0, 1], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [1, 11], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [2, 15], [1, 7], [2, 13], [3, 19], [1, 6], [3, 17], [2, 11], [3, 16], [1, 5], [4, 19], [3, 14], [2, 9], [3, 13], [4, 17], [1, 4], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [4, 13], [5, 16], [6, 19], [1, 3], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [5, 13], [7, 18], [2, 5], [7, 17], [5, 12], [8, 19], [3, 7], [7, 16], [4, 9], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [1, 2], [10, 19], [9, 17], [8, 15], [7, 13], [6, 11], [5, 9], [9, 16], [4, 7], [11, 19], [7, 12], [10, 17], [3, 5], [11, 18], [8, 13], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [2, 3], [13, 19], [11, 16], [9, 13], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [3, 4], [13, 17], [10, 13], [7, 9], [11, 14], [15, 19], [4, 5], [13, 16], [9, 11], [14, 17], [5, 6], [16, 19], [11, 13], [6, 7], [13, 15], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [1, 1]]), (20, [[0, 1], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [1, 11], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [2, 15], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [3, 17], [2, 11], [3, 16], [1, 5], [4, 19], [3, 14], [2, 9], [3, 13], [4, 17], [1, 4], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [4, 13], [5, 16], [6, 19], [1, 3], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [5, 13], [7, 18], [2, 5], [7, 17], [5, 12], [8, 19], [3, 7], [7, 16], [4, 9], [9, 20], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [1, 2], [10, 19], [9, 17], [8, 15], [7, 13], [6, 11], [11, 20], [5, 9], [9, 16], [4, 7], [11, 19], [7, 12], [10, 17], [3, 5], [11, 18], [8, 13], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [2, 3], [13, 19], [11, 16], [9, 13], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [3, 4], [13, 17], [10, 13], [7, 9], [11, 14], [15, 19], [4, 5], [13, 16], [9, 11], [14, 17], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [13, 15], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [1, 1]]), (21, [[0, 1], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [2, 15], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [4, 19], [3, 14], [2, 9], [3, 13], [4, 17], [5, 21], [1, 4], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [4, 13], [5, 16], [6, 19], [1, 3], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [2, 5], [7, 17], [5, 12], [8, 19], [3, 7], [7, 16], [4, 9], [9, 20], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [1, 2], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [6, 11], [11, 20], [5, 9], [9, 16], [4, 7], [11, 19], [7, 12], [10, 17], [3, 5], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [2, 3], [13, 19], [11, 16], [9, 13], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [3, 4], [16, 21], [13, 17], [10, 13], [7, 9], [11, 14], [15, 19], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [13, 15], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [1, 1]])], [(4, [[0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]]), (8, [[0, 1], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [3, 8], [2, 5], [3, 7], [1, 2], [4, 7], [3, 5], [5, 8], [2, 3], [5, 7], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [1, 1]]), (1, [[0, 1], [1, 1]]), (24, [[0, 1], [1, 24], [1, 23], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [2, 23], [1, 11], [2, 21], [1, 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[17, 24], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [19, 24], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [1, 1]]), (11, [[0, 1], [1, 11], [1, 10], [1, 9], [1, 8], [1, 7], [1, 6], [2, 11], [1, 5], [2, 9], [1, 4], [3, 11], [2, 7], [3, 10], [1, 3], [4, 11], [3, 8], [2, 5], [3, 7], [4, 9], [5, 11], [1, 2], [6, 11], [5, 9], [4, 7], [3, 5], [5, 8], [7, 11], [2, 3], [7, 10], [5, 7], [8, 11], [3, 4], [7, 9], [4, 5], [9, 11], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [1, 1]]), (12, [[0, 1], [1, 12], [1, 11], [1, 10], [1, 9], [1, 8], [1, 7], [1, 6], [2, 11], [1, 5], [2, 9], [1, 4], [3, 11], [2, 7], 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[7, 10], [12, 17], [17, 24], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [19, 24], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [1, 1]]), (4, [[0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]]), (6, [[0, 1], [1, 6], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3], [3, 4], [4, 5], [5, 6], [1, 1]]), (7, [[0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [2, 5], [3, 7], [1, 2], [4, 7], [3, 5], [2, 3], [5, 7], [3, 4], [4, 5], [5, 6], [6, 7], [1, 1]]), (8, [[0, 1], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [3, 8], [2, 5], [3, 7], [1, 2], [4, 7], [3, 5], [5, 8], [2, 3], [5, 7], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [1, 1]])], [(6, [[0, 1], [1, 6], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3], [3, 4], [4, 5], [5, 6], [1, 1]]), (14, [[0, 1], [1, 14], [1, 13], [1, 12], [1, 11], [1, 10], [1, 9], [1, 8], [1, 7], [2, 13], [1, 6], [2, 11], [1, 5], [3, 14], [2, 9], [3, 13], [1, 4], [3, 11], [2, 7], [3, 10], [4, 13], [1, 3], [5, 14], [4, 11], [3, 8], [5, 13], [2, 5], [5, 12], [3, 7], [4, 9], [5, 11], [6, 13], [1, 2], [7, 13], [6, 11], [5, 9], [4, 7], [7, 12], [3, 5], [8, 13], [5, 8], [7, 11], [9, 14], [2, 3], [9, 13], [7, 10], [5, 7], [8, 11], [3, 4], [10, 13], [7, 9], [11, 14], [4, 5], [9, 11], [5, 6], [11, 13], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [1, 1]]), (1, [[0, 1], [1, 1]]), (24, [[0, 1], [1, 24], [1, 23], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [2, 23], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [3, 23], [2, 15], [3, 22], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [4, 23], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [5, 24], [4, 19], [3, 14], [5, 23], [2, 9], [5, 22], [3, 13], [4, 17], [5, 21], [1, 4], [6, 23], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [7, 24], [5, 17], [3, 10], [7, 23], [4, 13], [5, 16], [6, 19], [7, 22], [1, 3], [8, 23], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [9, 23], [2, 5], [9, 22], [7, 17], [5, 12], [8, 19], [3, 7], [10, 23], [7, 16], [4, 9], [9, 20], [5, 11], [11, 24], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [11, 23], [1, 2], [12, 23], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [13, 24], [6, 11], [11, 20], [5, 9], [9, 16], [13, 23], [4, 7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [14, 23], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [15, 23], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [16, 23], [7, 10], [12, 17], [17, 24], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [19, 24], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [1, 1]]), (21, [[0, 1], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [2, 15], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [4, 19], [3, 14], [2, 9], [3, 13], [4, 17], [5, 21], [1, 4], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [4, 13], [5, 16], [6, 19], [1, 3], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [2, 5], [7, 17], [5, 12], [8, 19], [3, 7], [7, 16], [4, 9], [9, 20], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [1, 2], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [6, 11], [11, 20], [5, 9], [9, 16], [4, 7], [11, 19], [7, 12], [10, 17], [3, 5], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [2, 3], [13, 19], [11, 16], [9, 13], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [3, 4], [16, 21], [13, 17], [10, 13], [7, 9], [11, 14], [15, 19], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [13, 15], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [1, 1]]), (22, [[0, 1], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [2, 15], [3, 22], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [4, 19], [3, 14], [2, 9], [5, 22], [3, 13], [4, 17], [5, 21], [1, 4], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [4, 13], [5, 16], [6, 19], [7, 22], [1, 3], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [2, 5], [9, 22], [7, 17], [5, 12], [8, 19], [3, 7], [7, 16], [4, 9], [9, 20], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [1, 2], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [6, 11], [11, 20], [5, 9], [9, 16], [4, 7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [11, 14], [15, 19], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [1, 1]]), (23, [[0, 1], [1, 23], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [2, 23], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [3, 23], [2, 15], [3, 22], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [4, 23], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [4, 19], [3, 14], [5, 23], [2, 9], [5, 22], [3, 13], [4, 17], [5, 21], [1, 4], [6, 23], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [5, 17], [3, 10], [7, 23], [4, 13], [5, 16], [6, 19], [7, 22], [1, 3], [8, 23], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [9, 23], [2, 5], [9, 22], [7, 17], [5, 12], [8, 19], [3, 7], [10, 23], [7, 16], [4, 9], [9, 20], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [11, 23], [1, 2], [12, 23], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [6, 11], [11, 20], [5, 9], [9, 16], [13, 23], [4, 7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [14, 23], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [15, 23], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [16, 23], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [1, 1]]), (2, [[0, 1], [1, 2], [1, 1]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

SHA-256 / 1dc1d44b98bbdeb5bf910b30eedbbb17897ca81070d5d5b126e4499aee033fc1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x
    a,b,c,d=0,1,1,n
    out=[[0,1]]
    for _ in range(500):
     if c>n: break
     out.append([c,d])
     if d<=0: return None
     k=(n+b)//d
     a,b,c,d=c,d,k*c-a,k*d-b
     if a==1: break
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(2, [[0, 1], [1, 2], [1, 1]]), (1, [[0, 1], [1, 1]]), (24, [[0, 1], [1, 24], [1, 23], [1, 22], [1, 21], [1, 20], [1, 19], [1, 18], [1, 17], [1, 16], [1, 15], [1, 14], [1, 13], [1, 12], [2, 23], [1, 11], [2, 21], [1, 10], [2, 19], [1, 9], [2, 17], [1, 8], [3, 23], [2, 15], [3, 22], [1, 7], [3, 20], [2, 13], [3, 19], [1, 6], [4, 23], [3, 17], [2, 11], [3, 16], [4, 21], [1, 5], [5, 24], [4, 19], [3, 14], [5, 23], [2, 9], [5, 22], [3, 13], [4, 17], [5, 21], [1, 4], [6, 23], [5, 19], [4, 15], [3, 11], [5, 18], [2, 7], [7, 24], [5, 17], [3, 10], [7, 23], [4, 13], [5, 16], [6, 19], [7, 22], [1, 3], [8, 23], [7, 20], [6, 17], [5, 14], [4, 11], [7, 19], [3, 8], [8, 21], [5, 13], [7, 18], [9, 23], [2, 5], [9, 22], [7, 17], [5, 12], [8, 19], [3, 7], [10, 23], [7, 16], [4, 9], [9, 20], [5, 11], [11, 24], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21], [11, 23], [1, 2], [12, 23], [11, 21], [10, 19], [9, 17], [8, 15], [7, 13], [13, 24], [6, 11], [11, 20], [5, 9], [9, 16], [13, 23], [4, 7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [14, 23], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [15, 23], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [16, 23], [7, 10], [12, 17], [17, 24], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [19, 24], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [1, 1]]), (3, [[0, 1], [1, 3], [1, 2], [2, 3], [1, 1]]), (4, [[0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]]), (5, [[0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3], [3, 4], [4, 5], [1, 1]]), (6, [[0, 1], [1, 6], [1, 5], [1, 4], [1, 3], [2, 5], 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7], [11, 19], [7, 12], [10, 17], [13, 22], [3, 5], [14, 23], [11, 18], [8, 13], [13, 21], [5, 8], [12, 19], [7, 11], [9, 14], [11, 17], [13, 20], [15, 23], [2, 3], [15, 22], [13, 19], [11, 16], [9, 13], [16, 23], [7, 10], [12, 17], [5, 7], [13, 18], [8, 11], [11, 15], [14, 19], [17, 23], [3, 4], [16, 21], [13, 17], [10, 13], [17, 22], [7, 9], [18, 23], [11, 14], [15, 19], [4, 5], [17, 21], [13, 16], [9, 11], [14, 17], [19, 23], [5, 6], [16, 19], [11, 13], [17, 20], [6, 7], [19, 22], [13, 15], [20, 23], [7, 8], [15, 17], [8, 9], [17, 19], [9, 10], [19, 21], [10, 11], [21, 23], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [1, 1]]), (2, [[0, 1], [1, 2], [1, 1]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

SHA-256 / 98195138bcc194f4cf52ae2aa3aa516f1fca054186b543a1bfbd7b159a411ea1