#include using namespace std; #define int long long #define stoi stoll using ll=long long; using vi=vector; using pii=pair; #define ALL(c) begin(c),end(c) #define RALL(c) rbegin(c),rend(c) #define ITR(i,b,e) for(auto i=(b);i!=(e);++i) #define FORE(x,c) for(auto &x:c) #define REPF(i,a,n) for(int i=a,i##len=(int)(n);i=0;--i) #define SZ(c) ((int)c.size()) #define CONTAIN(c,x) (c.find(x)!=end(c)) #define OUTOFRANGE(y,x,h,w) ((y)<0||(x)<0||(y)>=(h)||(x)>=(w)) #define dump(...) const signed INF_=1001001001; const long long INF=1001001001001001001LL; const int DX[9]={0,1,0,-1,1,1,-1,-1,0},DY[9]={-1,0,1,0,-1,1,1,-1,0}; template ostream& operator<<(ostream &os,const vector &v) { ITR(i,begin(v),end(v))os<<*i<<(i==end(v)-1?"":" ");return os;} template istream& operator>>(istream &is,vector &v) { ITR(i,begin(v),end(v)) is>>*i;return is;} template istream& operator>>(istream &is, pair &p) { is>>p.first>>p.second;return is;} template bool chmax(T &a,const U &b){return a bool chmin(T &a,const U &b){return a>b?a=b,1:0;} template using heap=priority_queue,greater>; struct{template operator T(){T x;cin>>x;return x;}} IN; struct before_main_function { before_main_function() { cin.tie(0);ios::sync_with_stdio(false); cout<