#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #if __has_include() #include using namespace atcoder; #endif #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define _rep(i, n) _rep2(i, 0, n) #define _rep2(i, a, b) for(int i = (int)(a); i < (int)(b); i++) #define rep(...) GET_MACRO(__VA_ARGS__, _rep2, _rep)(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() using i64 = long long; template bool chmin(T& a, const U& b) { return (b < a) ? (a = b, true) : false; } template bool chmax(T& a, const U& b) { return (b > a) ? (a = b, true) : false; } inline void YesNo(bool f) { std::cout << (f? "Yes": "No") << std::endl; } templateistream& operator>>(istream&i,vector&v){rep(j,v.size())i>>v[j];return i;} templatestring join(vector&v){stringstream s;rep(i,v.size())s<<' '<ostream& operator<<(ostream&o,vector&v){if(v.size())o<string join(vector>&vv){string s="\n";rep(i,vv.size())s+=join(vv[i])+"\n";return s;} templateostream& operator<<(ostream&o,vector>&vv){if(vv.size())o< vector div(T x) { vector res; for(T i = 1; i * i <= x; i++) { if(x % i == 0) { res.push_back(i); if(i * i == x) break; res.push_back(x / i); } } sort(all(res)); return res; } i64 mypow(i64 a, i64 b){ i64 res = 1; while (b){ if (b & 1) res *= a; a *= a; b >>= 1; } return res; } int main(){ i64 n; cin >> n; if (n <= 2){ cout << n + 1 << endl; return 0; } auto z = div(n); i64 ans = 1e18; for (auto i: z){ i64 p = n / i - 1; if (p > i) chmin(ans, p); } for (i64 i = 1; i <= sqrt(n); i++){ i64 p = 1; for (i64 j = 1; ; j++){ p += mypow(i, j); if (n % p == 0){ i64 y = n / p; if (y < i){ cout << min(ans, i) << endl; return 0; } } } } cout << ans << endl; }