#include using namespace std; typedef pair pii; typedef long long ll; template using V = vector; template using VV = V>; #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i,n) rep2(i,0,n) #define rep2(i,m,n) for(int i=m;i<(n);i++) #define ALL(c) (c).begin(),(c).end() #define dump(x) cout << #x << " = " << (x) << endl constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); } template void chmin(T& t, const U& u) { if (t > u) t = u; } template void chmax(T& t, const U& u) { if (t < u) t = u; } template ostream& operator<<(ostream& os, const pair& p) { os<<"("< ostream& operator<<(ostream& os, const vector& v) { os<<"{"; rep(i, v.size()) { if (i) os<<","; os<