vector<vector<int>> capacity; // storing the capacity of each edge
vector<vector<int>> mat; // graph representation in adjacency matrix

// utilizing Breadth First Search (BFS) algorithm
int bfs(int s, int t, vector<int>& prev) {
    fill(prev.begin(), prev.end(), -1); // initalize previous nodes with -1
    prev[s] = -2;
    queue<pair<int, int>> q;
    q.push({s, INF});

    // while queue is not empty
    while (!q.empty()) {
        int cur = q.front().first;
        int flow = q.front().second;
        q.pop();

        for (int next : mat[cur]) {
            if (prev[next] == -1 && capacity[cur][next]) {
                prev[next] = cur;
                int new_flow = min(flow, capacity[cur][next]);
                if (next == t)
                    return new_flow;
                q.push({next, new_flow});
            }
        }
    }

    return 0;
}

// computing maximum flow in the graph
int maxflow(int s, int t) {
    int flow = 0;
    vector<int> prev(n);
    int new_flow;

    // doing BFS in each iteration, finding the shortest path available from 's' to 't'
    while (new_flow = bfs(s, t, prev)) {
        flow += new_flow;
        int cur = t;
        while (cur != s) {
            int prev = prev[cur];
            capacity[prev][cur] -= new_flow;
            capacity[cur][prev] += new_flow;
            cur = prev;
        }
    }

    return flow;
}