struct Dinic{
    struct Edge{
        int u, v;
        ll cap, flow = 0;
        Edge(int u, int v, ll cap) : u(u), v(v), cap(cap) {}
    };

    const ll flow_inf = 1e18;
    vector<Edge> edges;
    vector<vector<int>> adj;
    int n, m = 0;
    int s, t;
    vector<int> level, ptr;
    queue<int> q;

    Dinic(int n, int s, int t) : n(n), s(s), t(t){
        adj = vector<vector<int>>(n);
        level = vector<int>(n);
        ptr = vector<int>(n);
    }

    void add_edge(int u, int v, ll cap){
        edges.emplace_back(u, v, cap);
        edges.emplace_back(v, u, 0);
        adj[u].push_back(m);
        adj[v].push_back(m+1);
        m += 2;
    }

    bool bfs(){
        while(!q.empty()){
            int v = q.front();
            q.pop();
            for(int id : adj[v]){
                if(edges[id].cap == edges[id].flow) continue;
                if(level[edges[id].v] != -1) continue;
                level[edges[id].v] = level[v] + 1;
                q.push(edges[id].v);
            }
        }
        return level[t] != -1;
    }

    ll dfs(int v, ll pushed){
        if(!pushed) return 0;
        if(v == t) return pushed;

        for(int& cid = ptr[v]; cid < (int)adj[v].size(); cid++){
            int id = adj[v][cid];
            int u = edges[id].v;
            if(level[v] + 1 != level[u] || edges[id].cap == edges[id].flow) continue;
            ll tr = dfs(u, min(pushed, edges[id].cap - edges[id].flow));
            if(tr == 0) continue;
            edges[id].flow += tr;
            edges[id^1].flow -= tr;
            return tr;
        }
        return 0;
    }


    ll flow(){
        ll f = 0;
        while(true){
            fill(level.begin(), level.end(), -1);
            level[s] = 0;
            q.push(s);
            if(!bfs()) break;
            fill(ptr.begin(), ptr.end(), 0);
            while(ll pushed = dfs(s, flow_inf)){
                f += pushed;
            }
        }
        return f;
    }

};