Dinnic algorithm O(n^2*m)

import java.io.*;
import java.util.*;

public class Dinnic {
    FastScanner in;
    PrintWriter out;

    class Edge {
        int fr, to;
        int cost;
        int flow;
        Edge backEdge;

        public Edge(int fr, int to, int cost) {
            super();
            this.fr = fr;
            this.to = to;
            this.cost = cost;
            flow = 0;
        }

    }

    ArrayList<Edge>[] g;
    int[] d;
    int[] last;
    int n;

    boolean bfs() {
        Arrays.fill(d, -1);
        ArrayList<Integer> queue = new ArrayList<Integer>();
        int it = 0;
        queue.add(0);
        d[0] = 0;
        while (it < queue.size()) {
            int v = queue.get(it);
            for (Edge e : g[v]) {
                if (d[e.to] == -1 && e.flow < e.cost) {
                    d[e.to] = d[v] + 1;
                    queue.add(e.to);
                }
            }
            it++;
        }
        return d[n - 1] != -1;
    }

    int dfs(int v, int flow) {
        if (flow == 0 || v == n - 1) return flow;
        for (; last[v] < g[v].size(); last[v]++) {
            Edge e = g[v].get(last[v]);
            if (d[e.to] != d[v] + 1) continue;
            int pushed = dfs(e.to, Math.min(flow, e.cost - e.flow));
            if (pushed != 0) {
                e.flow += pushed;
                e.backEdge.flow -= pushed;
                return pushed;
            }
        }
        return 0;
    }

    void solve() {
        n = in.nextInt();
        int m = in.nextInt();
        g = new ArrayList[n];
        for (int i = 0; i < n; i++)
            g[i] = new ArrayList<Edge>();
        for (int i = 0; i < m; i++) {
            int fr = in.nextInt() - 1;
            int to = in.nextInt() - 1;
            int cost = in.nextInt();
            Edge e1 = new Edge(fr, to, cost);
            Edge e2 = new Edge(to, fr, 0);
            e1.backEdge = e2;
            e2.backEdge = e1;
            g[fr].add(e1);
            g[to].add(e2);
        }
        d = new int[n];
        last = new int[n];
        int flow = 0;
        while (bfs()) {
            while (true) {
                Arrays.fill(last, 0);
                int add = dfs(0, Integer.MAX_VALUE);
                if (add == 0) break;
                flow += add;
            }
        }
        out.println(flow);
    }

    void run() {
        try {
            in = new FastScanner(new File("maxflow.in"));
            out = new PrintWriter(new File("maxflow.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    public static void main(String[] args) {
        new Dinnic().run();
    }
}