#include <iostream> #include <vector> #include <algorithm> #include <cmath> using namespace std; typedef long long ll; // 快速幂取模 ll mod_pow(ll a, ll b, ll mod) { ll res = 1; while (b > 0) { if (b % 2 == 1) res = (res * a) % mod; a = (a * a) % mod; b /= 2; } return res; } // 质因数分解 vector<pair<ll, int>> factorize(ll n) { vector<pair<ll, int>> factors; for (ll i = 2; i * i <= n; ++i) { if (n % i == 0) { int cnt = 0; while (n % i == 0) { n /= i; cnt++; } factors.emplace_back(i, cnt); } } if (n > 1) factors.emplace_back(n, 1); return factors; } // 计算欧拉函数 ll euler_phi(ll n) { auto factors = factorize(n); ll res = n; for (auto [p, _] : factors) { res = res / p * (p - 1); } return res; } // 生成所有约数 vector<ll> get_divisors(ll n) { vector<ll> divisors; for (ll i = 1; i * i <= n; ++i) { if (n % i == 0) { divisors.push_back(i); if (i != n / i) divisors.push_back(n / i); } } sort(divisors.begin(), divisors.end()); return divisors; } int main() { ll N; cin >> N; ll phi = euler_phi(N); auto divisors = get_divisors(phi); for (auto d : divisors) { if (mod_pow(10, d, N) == 1) { cout << d << endl; return 0; } } // 如果没找到(理论上不可能) cout << phi << endl; return 0; }