/* -*- coding: utf-8 -*- * * 2177.cc: No.2177 Recurring ab - yukicoder */ #include #include using namespace std; /* constant */ const int MAX_N = 100; const int MAX_P = 1000000000; /* typedef */ typedef long long ll; /* global variables */ /* subroutines */ inline ll fp(int p, int na, int nb) { return (ll)p * p - (ll)na * p - nb; } /* main */ int main() { int n; scanf("%d", &n); // x=0.abab...[p] // (p^2)x=ab.abab.. -> (p^2-1)x=pa+b -> x=(pa+b)/(p^2-1) // x > 1/N -> Nx > 1 -> N{(pa+b)/(p^2-1)} > 1 -> N(pa+b) > p^2-1 // -> N(pa+b)+1>p^2 -> N(pa+b)>=p^2 -> p^2-Nap-Nb<=0 ll sum = 0; for (int a = 0; a <= 9; a++) for (int b = 0; b <= 9; b++) { if (a == b) continue; int na = n * a, nb = n * b; int r0 = na / 2, r1 = MAX_P + 1; while (r0 + 1 < r1) { int r = (r0 + r1) / 2; if (fp(r, na, nb) <= 0) r0 = r; else r1 = r; } int l0 = max(a, b), l1 = na / 2; while (l0 + 1 < l1) { int l = (l0 + l1) / 2; if (fp(l, na, nb) <= 0) l1 = l; else l0 = l; } //printf("l0=%d, r0=%d\n", l0, r0); if (l0 < r0) sum += r0 - l0; } printf("%lld\n", sum); return 0; }