A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Constraints

* $2 \leq |V| \leq 100$
* $1 \leq |E| \leq 1000$
* $0 \leq c_i \leq 10000$

Input

A flow network is given in the following format.

$|V|\;|E|$
$u_0\;v_0\;c_0$
$u_1\;v_1\;c_1$
:
$u_{|E|-1}\;v_{|E|-1}\;c_{|E|-1}$



$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., $|V|-1$. The source is 0 and the sink is $|V|-1$.

$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Example

Input

4 5
0 1 2
0 2 1
1 2 1
1 3 1
2 3 2


Output

3
// Java program for implementation of Ford Fulkerson algorithm
import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.LinkedList;

public class Main {
    static int V; //Number of vertices in graph
public static class FordFulkerson {

    /* Returns true if there is a path from source 's' to sink
    't' in residual graph. Also fills parent[] to store the
    path */
    boolean bfs(int rGraph[][], int s, int t, int parent[]) {
        // Create a visited array and mark all vertices as not
        // visited
        boolean visited[] = new boolean[V];
        for(int i=0; i<V; ++i)
            visited[i]=false;

        // Create a queue, enqueue source vertex and mark
        // source vertex as visited
        LinkedList<Integer> queue = new LinkedList<Integer>();
        queue.add(s);
        visited[s] = true;
        parent[s]=-1;

        // Standard BFS Loop
        while (queue.size()!=0)
        {
            int u = queue.poll();

            for (int v=0; v<V; v++)
            {
                if (visited[v]==false && rGraph[u][v] > 0)
                {
                    queue.add(v);
                    parent[v] = u;
                    visited[v] = true; 
                } 
            } 
        } 

        // If we reached sink in BFS starting from source, then 
        // return true, else false 
        return (visited[t] == true); 
    } 

    // Returns tne maximum flow from s to t in the given graph 
    int fordFulkerson(int graph[][], int s, int t) 
    { 
        int u, v; 

        // Create a residual graph and fill the residual graph 
        // with given capacities in the original graph as 
        // residual capacities in residual graph 

        // Residual graph where rGraph[i][j] indicates 
        // residual capacity of edge from i to j (if there 
        // is an edge. If rGraph[i][j] is 0, then there is 
        // not) 
        int rGraph[][] = new int[V][V]; 

        for (u = 0; u < V; u++) 
            for (v = 0; v < V; v++) 
                rGraph[u][v] = graph[u][v]; 

        // This array is filled by BFS and to store path 
        int parent[] = new int[V]; 

        int max_flow = 0; // There is no flow initially 

        // Augment the flow while tere is path from source 
        // to sink 
        while (bfs(rGraph, s, t, parent)) 
        { 
            // Find minimum residual capacity of the edhes 
            // along the path filled by BFS. Or we can say 
            // find the maximum flow through the path found. 
            int path_flow = Integer.MAX_VALUE; 
            for (v=t; v!=s; v=parent[v]) 
            { 
                u = parent[v]; 
                path_flow = Math.min(path_flow, rGraph[u][v]); 
            } 

            // update residual capacities of the edges and 
            // reverse edges along the path 
            for (v=t; v != s; v=parent[v]) 
            { 
                u = parent[v]; 
                rGraph[u][v] -= path_flow; 
                rGraph[v][u] += path_flow; 
            } 

            // Add path flow to overall flow 
            max_flow += path_flow; 
        } 

        // Return the overall flow 
        return max_flow; 
    } 
}
    // Driver program to test above functions 
    public static void main (String[] args) throws java.lang.Exception {
        Scanner sc = new Scanner(System.in);
        V = Integer.parseInt(sc.next());
        int E = Integer.parseInt(sc.next());
        int[][] graph = new int[V][V];
        for (int i=0;i<E;i++) {
            int s = Integer.parseInt(sc.next());
            int t = Integer.parseInt(sc.next());
            int c = Integer.parseInt(sc.next());
            graph[s][t] = c;
        }
        // System.out.println(Arrays.deepToString(graph));
        // int graph[][] =new int[][] { {0, 16, 13, 0, 0, 0}, 
        //                             {0, 0, 10, 12, 0, 0}, 
        //                             {0, 4, 0, 0, 14, 0}, 
        //                             {0, 0, 9, 0, 0, 20}, 
        //                             {0, 0, 0, 7, 0, 4}, 
        //                             {0, 0, 0, 0, 0, 0} 
        //                         }; 
        FordFulkerson m = new FordFulkerson(); 

        // System.out.println("The maximum possible flow is " + 
                        // m.fordFulkerson(graph, 0, V-1));
        System.out.println(m.fordFulkerson(graph, 0, V-1));

    }
}
