const int Maxn = 1e5;
const int Maxm = 1e5;
const LL Inf = 0x3f3f3f3f;

struct edge {
    int to[Maxm * 2 + 5], Next[Maxm * 2 + 5]; LL val[Maxm * 2 + 5];
    int len, Head[Maxn + 5];
    edge () { len = 1; memset (Head, 0, sizeof Head); }
    void Init () {
        len = 1;
        memset (Head, 0, sizeof Head);
    }
    void plus (int x, int y, LL w) {
        to[++len] = y;
        Next[len] = Head[x];
        val[len] = w;
        Head[x] = len;
    }
    void add (int x, int y, LL w) {
        plus (x, y, w); plus (y, x, 0);
    }
    void rev_add (int x, int y, LL w) {
        plus (y, x, w); plus (x, y, 0);
    }
};
struct Max_Flow {
	int s, t;
	edge mp;

	int hh, tt, q[Maxn + 5];
	int depth[Maxn + 5], cur[Maxn + 5];
	bool BFS () {
	    rep (i, 1, tt) depth[q[i]] = 0;
	    hh = 1; tt = 0; q[++tt] = s;
	    depth[s] = 1; cur[s] = mp.Head[s];
	    while (hh <= tt) {
	        int u = q[hh++];
	        for (int i = mp.Head[u]; i; i = mp.Next[i]) {
	            int v = mp.to[i]; LL w = mp.val[i];
	            if (w == 0) continue;
	            if (depth[v]) continue;
	            depth[v] = depth[u] + 1;
	            cur[v] = mp.Head[v];
	            q[++tt] = v;
	            if (v == t) return 1;
	        }
	    }
	    return 0;
	}
	LL DFS (int u, LL Up) {
	    if (u == t) return Up;
	    if (Up == 0) return 0;
	    LL flow = 0;
	    while (cur[u] && flow < Up) {
	        int i = cur[u]; cur[u] = mp.Next[cur[u]];
	        int v = mp.to[i]; LL w = mp.val[i];
	        if (w == 0) continue;
	        if (depth[v] != depth[u] + 1) continue;
	        LL tmp = DFS (v, Min (Up - flow, w));
	        if (tmp == 0) depth[v] = -1;
	        flow += tmp; mp.val[i] -= tmp; mp.val[i ^ 1] += tmp;
	        if (mp.val[i] && flow >= Up) cur[u] = i;
	    }
	    return flow;
	}
	LL Dinic () {
	    LL flow = 0;
	    while (BFS ()) {
	        flow += DFS (s, Inf);
	    }
	    return flow;
	}
};