#include using namespace std; using ll=long long; #define int ll #define rng(i,a,b) for(int i=int(a);i=int(a);i--) #define per(i,b) gnr(i,0,b) #define pb push_back #define eb emplace_back #define a first #define b second #define bg begin() #define ed end() #define all(x) x.bg,x.ed #ifdef LOCAL #define dmp(x) cerr<<__LINE__<<" "<<#x<<" "< void chmax(t&a,u b){if(a void chmin(t&a,u b){if(b using vc=vector; template using vvc=vc>; using pi=pair; using vi=vc; template ostream& operator<<(ostream& os,const pair& p){ return os<<"{"< ostream& operator<<(ostream& os,const vc& v){ os<<"{"; for(auto e:v)os< void dmpr(ostream&os,const T&t,const Args&... args){ os< void print_tuple(ostream&,const T&){ } template void print_tuple(ostream&os,const T&t){ if(i)os<<","; os<(t); print_tuple(os,t); } template ostream& operator<<(ostream&os,const tuple&t){ os<<"{"; print_tuple<0,tuple,Args...>(os,t); return os<<"}"; } void print(ll x,int suc=1){ cout<>i; return i; } vi readvi(int n,int off=0){ vi v(n); rep(i,n)v[i]=read()+off; return v; } template void print(const vector&v,int suc=1){ rep(i,v.size()) print(v[i],i==int(v.size())-1?suc:2); } string readString(){ string s; cin>>s; return s; } template T sq(const T& t){ return t*t; } //#define CAPITAL void yes(bool ex=true){ #ifdef CAPITAL cout<<"YES"< void mkuni(vc&v){ sort(all(v)); v.erase(unique(all(v)),v.ed); } ll rand_int(ll l, ll r) { //[l, r] #ifdef LOCAL static mt19937_64 gen; #else static random_device rd; static mt19937_64 gen(rd()); #endif return uniform_int_distribution(l, r)(gen); } template int lwb(const vc&v,const t&a){ return lower_bound(all(v),a)-v.bg; } //ARC055D int gcd(int a,int b){return b?gcd(b,a%b):a;} /*int gcd(int a,int b){ if(a==0)return b; if(b==0)return a; if(a<0)a=-a; if(b<0)b=-b; int s=botbit(a|b); a>>=botbit(a); do{ b>>=botbit(b); if(a>b)swap(a,b); b-=a; }while(b); return a< x = p mod q //returns (-1,-1) when infeasible pi crt(int a,int b,int c,int d){ if(b>x>>y; //tie(a,b)=crt(a,b,x,y); tie(a,b)=crt(x,y,a,b); if(a==-1)break; } if(a==0)a+=b; cout<