#include <iostream>
#include <string>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#define LL long long
#define inf 0x3f3f3f3f
#define fr first
#define sc second
#define range(i,a,b) for(auto i=a;i<=b;++i)
#define itrange(i,a,b) for(auto i=a;i!=b;++i)
#define rerange(i,a,b) for(auto i=a;i>=b;--i)
#define fill(arr,tmp) memset(arr,tmp,sizeof(arr))
using namespace std;
const int Vmxn=int(1e5+5);
namespace MCMF{
struct edge{
int from,to,cap,flow,cost;
edge(int u,int v,int c,int f,int w):from(u),to(v),cap(c),flow(f),cost(w){}
};
int n,m;
vector<edge>edges;
vector<int>G[Vmxn];
bool inq[Vmxn];
int d[Vmxn],p[Vmxn],a[Vmxn];
void init(int sz){
n=sz;
range(i,0,n)G[i].clear();
edges.clear();
}
void add_edge(int from,int to,int cap,int cost){
edges.emplace_back((edge(from,to,cap,0,cost));
edges.emplace_back(edge(to,from,0,0,-cost));
m=int(edges.size());
G[from].push_back(m-2);
G[to].push_back(m-1);
}
bool spfa(int s,int t,int&flow,LL&cost){
fill(d,inf);fill(inq,0);
d[s]=0;inq[s]=true;p[s]=0;a[s]=inf;
queue<int>q;
q.push(s);
while(not q.empty()){
int u=q.front();
q.pop();
inq[u]=0;
range(i,0,G[u].size()-1){
edge& e=edges[G[u][i]];
if(e.cap>e.flow and d[e.to]>d[u]+e.cost){
d[e.to]=d[u]+e.cost;
p[e.to]=G[u][i];
a[e.to]=min(a[u],e.cap-e.flow);
if(not inq[e.to]){
q.push(e.to);
inq[e.to]=true;
}
}
}
if(d[t]==inf)return false;
flow+=a[t];
cost+=1LL*d[t]*a[t];
for(int u=t;u!=s;u=edges[p[u]].from){
edges[p[u]].flow+=a[t];
edges[p[u]^1].flow-=a[t];
}
return true;
}
}
int MincostMaxflow(int s,int t,LL&cost){
int flow=0;
cost=0;
while(spfa(s,t,flow,cost));
return flow;
}
}
void init(){
}
void solve(){
}
int main() {
init();
solve();
return 0;
}