#include using namespace std; #if __has_include() #include using namespace atcoder; templateistream &operator>>(istream &is,static_modint &a){long long b;is>>b;a=b;return is;} istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;} #endif #ifdef LOCAL #include "debug.h" #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) templateostream &operator<<(ostream &os,const pair&p){os<; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templateistream &operator>>(istream &is,pair&p){is>>p.first>>p.second;return is;} templateistream &operator>>(istream &is,vector &a){for(auto &i:a)is>>i;return is;} templatevoid operator++(pair&a,int n){a.first++,a.second++;} templatevoid operator--(pair&a,int n){a.first--,a.second--;} templatevoid operator++(vector&a,int n){for(auto &i:a)i++;} templatevoid operator--(vector&a,int n){for(auto &i:a)i--;} #define reps(i,a,n) for(int i=(a);i<(n);i++) #define rep(i,n) reps(i,0,n) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcount(x) ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } void SOLVE(); int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); #ifdef LOCAL clock_t start=clock(); #endif int testcase=1; //cin>>testcase; for(int i=0;iprm{2,3,5,7,11,13,17,19,23,29,31,37}; ll sqmod(ll a,ll p){ __int128_t r=a; r*=r; r%=p; return (ll)r; } ll func(ll a,ll p,int c){ __int128_t r=a; r*=r; r+=c; r%=p; return (ll)r; } ll powmod(ll a,ll b,ll p){ if(b==0)return 1ll; if(b==1)return a; __int128_t r=powmod(a,b/2,p); r*=r; r%=p; if(b%2==1)r*=(__int128_t)a; r%=p; return (ll)r; } bool primeJudge(ll x){ if(x==1)return false; if(binary_search(all(prm),x))return true; if(x%2==0)return false; ll d=x-1; int s=0; while(d%2==0){ d/=2; s++; } for(int i:prm){ ll h=powmod(i,d,x); bool ok=false; if(h==1||h==x-1)continue;; rep(j,s){ h=sqmod(h,x); if(h==x-1)ok=true; } if(!ok)return false; } return true; } ll divisor(ll n){ if(n%2==0)return 2ll; ll x=0,y=0; int c=1; while(true){ x=func(x,n,c); y=func(func(y,n,c),n,c); ll g=gcd(abs(x-y),n); if(g==n){ c++; x=0; y=0; continue; } if(g>1)return g; } } vectorprimefactor(ll n){ if(primeJudge(n))return (vector){n}; if(n==1)return (vector){1}; queueque; que.push(n); vectorans; while(!que.empty()){ ll x=que.front(); que.pop(); ll y=divisor(x); if(primeJudge(y))ans.push_back(y); else que.push(y); x/=y; if(x==1)continue; if(primeJudge(x))ans.push_back(x); else que.push(x); } return ans; } void SOLVE(){ int n; cin>>n; rep(i,n){ ll x; cin>>x; cout<