#include "bits/stdc++.h" #define REP(i,num) for(ll i=0;i<(num);++i) #define FOR(i,c,num) for(ll (i)=(c);(i)<(num);++(i)) #define LOOP(i) while(i--) #define ALL(c) c.begin(),c.end() #define PRINTALL(c) for(auto pitr=c.begin();pitr!=c.end();++pitr){cout<<*pitr;if(next(pitr,1)!=c.end())cout<<' ';}cout<& lhs,const pair& rhs){return lhs.c comp rhs.c;} using namespace std; using ll = long long; using vll = vector; using vvll = vector>; constexpr ll atcoder_mod = 1e9+7; template T in(){ T x; cin >> x; return (x); } template> C vecin(int N){ C x(N);REP(i,N){ x[i]=in(); }return x; } void vout(){ cout << endl; } template void vout(Head&& h,Tail&&... t){ cout << ' ' << h;vout(forward(t)...); } void out(){ cout << endl; } template void out(Head&& h,Tail&&... t){ cout << h;vout(forward(t)...); } template bool chmax(T& a,T b){ if(a bool chmin(T& a,T b){ if(a>b){ a=b;return true; }return false; } ll extend_gcd(ll a,ll b,ll &x,ll &y){ if(b==0){ x = 1; y = 0; return a; } ll d = extend_gcd(b,a%b,y,x); y -= a/b * x; return d; } ll safemod(ll a,ll m){ return (a%m+m)%m; } ll modinv(ll a,ll m){ ll x,y; extend_gcd(a,m,x,y); return safemod(x,m); } ll powermod(ll a,ll b,ll m){ if(b==0){ return 1LL; } if(b%2){ return (a*powermod(a,b-1LL,m))%m; } return powermod((a*a)%m,b/2LL,m); } int main(){ cin.tie(0); ios::sync_with_stdio(false); cout<