#include <bits/stdc++.h> using namespace std; void Yes(){cout << "YES\n";} void No(){cout << "NO\n";} struct Montgomery{ //2^62未満&奇数modのみ. //初めにsetmodする. using u64 = uint64_t; using u128 = __uint128_t; private: static u64 mod,N2,Rsq; //N*N2≡1(mod N); //Rsq = R^2modN; R=2^64. u64 v = 0; public: long long val(){return reduce(v);} u64 getmod(){return mod;} static void setmod(u64 m){ assert(m<(1LL<<62)&&(m&1)); mod = m; N2 = mod; for(int i=0; i<5; i++) N2 *= 2-N2*mod; Rsq = (-u128(mod))%mod; } //reduce = T*R^-1modNを求める. u64 reduce(const u128 &T){ //T*R^-1≡(T+(T*(-N2))modR*N)/R 2N未満なので-N必要かだけで良い. u64 ret = (T+u128(((u64)T)*(-N2))*mod)>>64; if(ret >= mod) ret -= mod; return ret; } //初期値<mod. 初めにw*R modN...->reduce(R^2)でok. Montgomery(){v = 0;} Montgomery(long long w):v(reduce(u128(w)*Rsq)){} Montgomery& operator=(const Montgomery &b) = default; Montgomery operator-()const{return Montgomery()-Montgomery(*this);} Montgomery operator+(const Montgomery &b)const{return Montgomery(*this)+=b;} Montgomery operator-(const Montgomery &b)const{return Montgomery(*this)-=b;} Montgomery operator*(const Montgomery &b)const{return Montgomery(*this)*=b;} Montgomery operator/(const Montgomery &b)const{return Montgomery(*this)/=b;} Montgomery& operator+=(const Montgomery &b){ v += b.v; if(v >= mod) v -= mod; return (*this); } Montgomery& operator-=(const Montgomery &b){ v += mod-b.v; if(v >= mod) v -= mod; return (*this); } Montgomery& operator*=(const Montgomery &b){ v = reduce(u128(v)*b.v); return (*this); } Montgomery& operator/=(const Montgomery &b){ (*this) *= b.inv(); return (*this); } Montgomery pow(u64 b)const{ Montgomery ret = 1,p = (*this); while(b){ if(b&1) ret *= p; p *= p; b >>= 1; } return ret; } Montgomery inv()const{return pow(mod-2);} bool operator!=(const Montgomery &b){return v!=b.v;} bool operator==(const Montgomery &b){return v==b.v;} }; typename Montgomery::u64 Montgomery::mod,Montgomery::N2,Montgomery::Rsq; using mont = Montgomery; bool MillerRabin(long long N,const vector<long long> &A){ mont::setmod(N); long long s = __builtin_ctzll(N-1),d = N-1; d >>= s; for(auto &a : A){ if(N <= a) break; mont x = mont(a).pow(d); if(x != 1){ long long t; for(t=0; t<s; t++){ if(x == N-1) break; x *= x; } if(t == s) return false; } } return true; } bool isprime(const long long N){ if(N <= 1) return false; else if(N == 2) return true; else if(N%2 == 0) return false; else if(N < 4759123141LL) return MillerRabin(N,{2,7,61}); else return MillerRabin(N, {2,325,9375,28178,450775,9780504,1795265022}); } int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int N; cin >> N; int phi = N,n = N; for(int i=2; i*i<=n; i++){ if(n%i) continue; phi -= phi/i; while(n%i == 0) n /= i; } if(n != 1) phi -= phi/n; vector<int> D; for(int i=1; i*i<=phi; i++){ if(phi%i == 0) D.push_back(i); if(i*i != phi) D.push_back(phi/i); } sort(D.begin(),D.end()); mont::setmod(N); for(auto d : D){ mont now = mont(10).pow(d); if(now == 1){cout << d << endl; break;} } }