#include "bits/stdc++.h" #include <stdio.h> #include <math.h> #include "atcoder/all" #include <float.h> #include <boost/multiprecision/cpp_int.hpp> using namespace boost::multiprecision; using namespace std; using namespace atcoder; using ll = long long; using ull = unsigned long long; using mint = modint998244353; using mint2 = modint1000000007; const double eps = 1e-9; #define OVERLOAD3(_1, _2, _3, call,...) call #define REP0(n) for (ll i = 0; i < ll(n); ++i) #define REP1(i, n) for (ll i = 0; i < ll(n); ++i) #define REP2(i, a, b) for (ll i = ll(a); i < ll(b); ++i) #define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__) #define RREP0(n) for (ll i = ll(n) - 1; i >= 0; --i) #define RREP1(i, n) for (ll i = ll(n) - 1; i >= 0; --i) #define RREP2(i, a, b) for (ll i = ll(a) - 1; i >= b; --i) #define RREP(...) OVERLOAD3(__VA_ARGS__, RREP2, RREP1, RREP0)(__VA_ARGS__) #define REPE(i, c) for (const auto& i : c) #define TCASE() ll _ttt; cin >> _ttt; while(_ttt--) template<class... T> void COMMON_IN(T&... a) { (cin >> ... >> a); } #define LI(...) ll __VA_ARGS__; COMMON_IN(__VA_ARGS__); using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; #define VLI(a, n) vector<ll> a; a.assign(n, 0); for(auto& x : a) cin >> x; #define DLI(a, n) deque<ll> a; a.assign(n, 0); for(auto& x : a) cin >> x; #define VSI(a, n) vector<string> a; a.assign(n, ""); for(auto& x : a) cin >> x; #define VVLI(a, n, m) vector<vector<ll>> a(n, vector<ll>(m)); for(auto& x : a) for(auto& y : x) cin >> y; using vd = vector<double>; using pl = pair<ll, ll>; using vpl = vector<pl>; struct uv { ll u; ll v; ll c; }; #define VUVI(a, n) vector<uv> a; a.assign(n, {0, 0, 1}); for(auto& x : a) {cin >> x.u >> x.v; x.u--; x.v--;} #define VUVCI(a, n) vector<uv> a; a.assign(n, {0, 0, 0}); for(auto& x : a) {cin >> x.u >> x.v >> x.c; x.u--; x.v--;} vvl to_edge(const ll n, const vector<uv>& v) { vvl ret(n); for (auto& x : v) ret[x.u].push_back(x.v); return ret; } vvl to_edge_d(const ll n, const vector<uv>& v) { vvl ret(n); for (auto& x : v) { ret[x.u].push_back(x.v); ret[x.v].push_back(x.u); } return ret; } template <class T = long long> using pql = priority_queue<T>; template <class T = long long> using pqg = priority_queue<T, vector<T>, greater<T>>; using vm = vector<mint>; using vvm = vector<vm>; ostream& operator<<(ostream& os, const mint& v) { os << v.val(); return os; } void yn(bool f) { std::cout << (f ? "Yes" : "No") << "\n"; }; template<class T> void ov(const T& v) { for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) cout << " "; cout << *it; } }; template<> void ov(const vm& v) { for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) cout << " "; cout << it->val(); } }; const ll llhuge = 1LL << 61; //十分でかいが多少足しても溢れない数値 auto gmax(const auto& a, const auto& b) { return a > b ? a : b; }; auto gmin(const auto& a, const auto& b) { return a < b ? a : b; }; bool chmin(auto& a, const auto& b) { const auto olda = a; a = gmin(a, b); return olda != a; } bool chmax(auto& a, const auto& b) { const auto olda = a; a = gmax(a, b); return olda != a; } void sort(auto& v) { std::ranges::sort(v); }; void rev(auto& v) { std::ranges::reverse(v); }; template<class T> auto p_sum(const T& v) { T ret(v.size()); std::partial_sum(begin(v), end(v), ret.begin()); return ret; }; template<class T, class K = T::key_type, class V = T::mapped_type> [[nodiscard]] V myat(const T& mp, const K& key) { return mp.find(key) == mp.end() ? V() : mp.at(key); } long long ceil(const long long a, const long long b) { return (a + b - 1) / b; } int euler_phi(int n) { int res = n; for (int x = 2; x * x <= n; ++x) { if (n % x == 0) { res = res / x * (x - 1); while (n % x == 0) { n /= x; } } } if (n > 1) { res = res / n * (n - 1); } return res; } // ab mod m (m < 10^13) を求める constexpr unsigned long long prod_mod(unsigned long long a, unsigned long long b, unsigned long long m) { constexpr unsigned long long mask{ 1048575 }; unsigned long long a_high{ a >> 40 }, a_mid{ (a >> 20) & mask }, a_low{ a & mask }; unsigned long long r{}; (r += b * a_high) %= m; (r <<= 20) %= m; (r += b * a_mid) %= m; (r <<= 20) %= m; (r += b * a_low) %= m; return r; } // a^b mod m を求める constexpr unsigned long long pow_mod(unsigned long long a, unsigned long long b, unsigned long long m) { unsigned long long r{ 1 }; while (b) { if (b & 1) r = prod_mod(r, a, m); a = prod_mod(a, a, m); b /= 2; } return r; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); LI(n); if (n == 1) { cout << 1 << "\n"; return 0; } ll phi = euler_phi(n); vl div; div.reserve(phi); for (long long i = 1; i * i <= phi; i++) { if (phi % i != 0) continue; if (i * i != phi) div.push_back(phi / i); if (pow_mod(10, i, n) == 1) { cout << i << "\n"; return 0; } } RREP(i, div.size()) { if (pow_mod(10, div[i], n) == 1) { cout << div[i] << "\n"; return 0; } } }