return [=[
struct mcmf {
    struct edge {
        int to;
        ll cap;
        ll flow;
        ll cost;
        int rev;
        int mark;
    };
    vector<vector<edge>> edges;
    vector<ll> dis;
    vector<bool> vis;
    ll ret;
    mcmf(int n) : edges(n + 1), dis(n + 1), vis(n + 1) {}
    void add_edge(int from, int to, ll cap, ll cost, int mark = 0, int mark_rev = 0) {
        edges[from].push_back({ to, cap, 0, cost, int(edges[to].size()), mark });
        edges[to].push_back({ from, 0, 0, -cost, int(edges[from].size() - 1), mark_rev });
    }
    bool sp(int s, int t) {
        dis.assign(edges.size(), INFLL);
        dis[s] = 0;
        int n = edges.size();
        int f = 1;
        while (f) {
            f = 0;
            for (int i = 0; i < n; ++i) {
                for (auto&& [to, cap, flow, cost, rev, mark] : edges[i]) {
                    if (cap > flow and dis[to] > dis[i] + cost) {
                        dis[to] = dis[i] + cost;
                        f = 1;
                    }
                }
            }
        }
        return dis[t] != INFLL;
    }
    ll dfs(int s, int t, ll cap) {
        if (vis[s]) {
            return 0;
        }
        vis[s] = 1;
        if (s == t) {
            return cap;
        }
        ll res = 0;
        int n = edges[s].size();
        for (int i = 0; i < n; ++i) {
            auto e = edges[s][i];
            if (e.cap > e.flow and dis[e.to] == dis[s] + e.cost) {
                ll nw = dfs(e.to, t, min(cap - res, e.cap - e.flow));
                edges[s][i].flow += nw;
                edges[e.to][e.rev].flow -= nw;
                res += nw;
                ret += nw * e.cost;
                if (res == cap) {
                    return res;
                }
            }
        }
        return res;
    }
    // returns: (flow, cost)
    pll run(int s, int t) {
        ll res = 0; ret = 0;
        while (sp(s, t)) {
            vis.assign(edges.size(), 0);
            ll curr = dfs(s, t, LLONG_MAX);
            res += curr;
            // BUG: this is a temporary fix of the infinite-looping issue observed
            // when dealing with networks with negative weights.
            if (curr == 0) break;
        }
        return { res, ret };
    }
};

]=]