#include //#include //#include //#include #define rep(i, a) for (int i = (int)0; i < (int)a; ++i) #define rrep(i, a) for (int i = (int)a - 1; i >= 0; --i) #define REP(i, a, b) for (int i = (int)a; i < (int)b; ++i) #define RREP(i, a, b) for (int i = (int)a - 1; i >= b; --i) #define repl(i, a) for (ll i = (ll)0; i < (ll)a; ++i) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define popcount __builtin_popcount #define popcountll __builtin_popcountll #define fi first #define se second using ll = long long; constexpr ll mod = 1e9 + 7; constexpr ll mod_998244353 = 998244353; constexpr ll INF = 1LL << 60; // #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") //using lll=boost::multiprecision::cpp_int; //using Double=boost::multiprecision::number>;//仮数部が1024桁 template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template T mypow(T x, T n, const T &p = -1) { //x^nをmodで割った余り if (p != -1) { x =(x%p+p)%p; } T ret = 1; while (n > 0) { if (n & 1) { if (p != -1) ret = (ret * x) % p; else ret *= x; } if (p != -1) x = (x * x) % p; else x *= x; n >>= 1; } return ret; } using namespace std; //using namespace atcoder; void solve() { ll n; cin>>n; if(n==1){ cout<<2<<"\n"; return; }else if(n==2){ cout<<3<<"\n"; return; } ll ans=n-1; auto check=[n](ll i,int j)->ll{ ll l=2,r=n; constexpr ll maxv=INF; while(r-l>1){ ll mid=(l+r)/2; ll x=1; bool ng=false; rep(num,j){ if(x<=maxv/mid)x*=mid; else if(num!=j-1){ ng=true; break; } } if(ng){ r=mid; continue; } if((x-1)/(mid-1)<=i&&(x-1)<=i*(mid-1))l=mid;//前半はオーバーフロー対策,後半は切り捨ての関係 else r=mid; } ll x=1; rep(num,j){ if(x<=maxv/l)x*=l; else if(num!=j-1){ return INF; } } if((x-1)%(l-1))return INF; ll val=(x-1)/(l-1); if(val==i&&n/val<=l-1)return l; else return INF; }; for(ll i=1;i*i<=n;++i){ if(n%i==0){ rep(j,41){ chmin(ans,check(i,j)); } if(i*i!=n){ rep(j,41){ chmin(ans,check(n/i,j)); } } } } cout<