Problem: Niwel is a little golden bear. As everyone knows, bears live in forests, but Niwel got tired of seeing all the trees so he decided to move to the city.

In the city, Niwel took on a job managing bears to deliver goods. The city that he lives in can be represented as a directed graph with n nodes and m edges. Each edge has a weight capacity. A delivery consists of a bear carrying weights with their bear hands on a simple path from node 1 to node n. The total weight that travels across a particular edge must not exceed the weight capacity of that edge.

Niwel has exactly x bears. In the interest of fairness, no bear can rest, and the weight that each bear carries must be exactly the same. However, each bear may take different paths if they like.

Niwel would like to determine, what is the maximum amount of weight he can deliver (it's the sum of weights carried by bears). Find the maximum weight.

Input

The first line contains three integers n, m and x (2 ≤ n ≤ 50, 1 ≤ m ≤ 500, 1 ≤ x ≤ 100 000) — the number of nodes, the number of directed edges and the number of bears, respectively.

Each of the following m lines contains three integers ai, bi and ci (1 ≤ ai, bi ≤ n, ai ≠ bi, 1 ≤ ci ≤ 1 000 000). This represents a directed edge from node ai to bi with weight capacity ci. There are no self loops and no multiple edges from one city to the other city. More formally, for each i and j that i ≠ j it's guaranteed that ai ≠ aj or bi ≠ bj. It is also guaranteed that there is at least one path from node 1 to node n.

Output

Print one real value on a single line — the maximum amount of weight Niwel can deliver if he uses exactly x bears. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct if <image>.

Examples

Input

4 4 3
1 2 2
2 4 1
1 3 1
3 4 2


Output

1.5000000000


Input

5 11 23
1 2 3
2 3 4
3 4 5
4 5 6
1 3 4
2 4 5
3 5 6
1 4 2
2 5 3
1 5 2
3 2 30


Output

10.2222222222

Note

In the first sample, Niwel has three bears. Two bears can choose the path <image>, while one bear can choose the path <image>. Even though the bear that goes on the path <image> can carry one unit of weight, in the interest of fairness, he is restricted to carry 0.5 units of weight. Thus, the total weight is 1.5 units overall. Note that even though Niwel can deliver more weight with just 2 bears, he must use exactly 3 bears on this day.

Solution (in JAVA):

Solution:
/*
     D    A    R    K    L      _                 _         O    R    D    D    A
         K                    / |                 | \        L    O    R         D
        A         R         _ / |                 | \ _       K    L         O    R
  D         A    R    K     _ / |         _       | \ _        L    O    R    D    D
      R    K    L       _ / _   |       _ | \\    |   _ \       O    R    D    D
     R         K        _ / _   |       _ | \ \   |   _ \        L    O    R
    D    A    R     _ / _ / |   /     /         \ \   | \ _ \ _        K    L    O
   D    D           _ / _ / |   /     /          \ \   | \ _ \ _             A
       K        _ / _ /     | /     /     _       \ \ |     \ _ \ _      L    O    R
 D    A        _ / _ /      | /     /     _       \ \ |      \ _ \ _      R         K
            _ / _ /         | |     |   |   \ (O) / | |         \ _ \ _         O
    D      _ / _ /          | |     |   |    \   /  | |          \ _ \ _         D
   A      / _ /     |   |   | \     |   \ _   \|/   / |   |   |     \ _ \
  K      / _ /      |   |   | \     |   \ _    V    / |   |   |      \ _ \         L
        / /         |   |   |   \ _ /       \ _ _ /   |   |   |         \ \
       / /          |   |   |                         |   | | |          \ \
      / /       |   | | \     \       ROWECHEN      /     / | |   |       \ \
     / /    _ _ |   | | \     \        ZHONG        /     / | |   | _ _    \ \
    / / _ /   \ | | | |   \ / \ \                 / / \ /   | | | | /   \ _ \ \
   / / _ /    \ | | | |       \ \                 / /       | | | | /    \ _ \ \
  / / /         \ \ \ \ /       /                 \       \ / / / /         \ \ \
 \ / /          \ \ \ \ /       /                 \       \ / / / /          \ \ /
  \|/             \|/         |         |         |           \|/             \|/
  L         O     \|/         |         |   |     |           \|/        R    D
 A    R    K    L             / _ |     |   | _     \      O    R    D    D    A    R
     L    O         R         / _ |     |   | _     \       D    D         A    R
    L    O    R    D        / / / _     | _ | | \ _   \      D    A    R         K
   O    R    D              / / / _ |   | _ | | \ _   \       D    A    R    K    L
  R    D    D    A    R     | / / | | / | | \ / | | \ |        K    L    O    R    D
 A         R         K      | / / | | / | | \ / | | \ |              L    O         R
     D    A         R         /   \ / | | | / | | / \ /     K    L         O    R
         D    D         A     /   \ / | | | / | | / \/            R    K    L    O
             R         D    D     / | / \ |   \ /        A    R    K    L    O    R
       D    A    R    K    L      / | / \ |    \/              O    R    D    D
 R    K    L    O    R    D       \ /     |      D    A    R         K    L    O    R
          D    A    R             \/      |            K    L    O    R    D    D

*/
//TEMPLATE V2

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

public class D653 {
    //Solution goes below: ------------------------------------
    public boolean bfs(int src, int sink, int[] parents, int[] maxFlow) {
        Arrays.fill(parents, -1);
        Arrays.fill(maxFlow, -1);

        Queue<Integer> q = new LinkedList<>();
        q.add(src);
        maxFlow[src] = Integer.MAX_VALUE;
        boolean exists = false;

        while (!q.isEmpty()) {
            int location = q.remove();
            int flow = maxFlow[location];

            exists |= (location == sink);

            for (int i = 0; i < graph.length; i++) {
                int capacity = graph[location][i];

                if (parents[i] == -1 && capacity > 0) {
                    parents[i] = location;
                    maxFlow[i] = Math.min(flow, capacity);

                    q.add(i);
                }
            }
        }

        return exists;
    }

    public int getFlow(int src, int sink) {
        int flow = 0;
        int[] maxFlow = new int[graph.length];
        int[] parents = new int[graph.length];

        while (bfs(src, sink, parents, maxFlow)) {
            int currentFlow = maxFlow[sink];
            flow += currentFlow;

            int node = sink;
            while (node != src) {
                int parentNode = parents[node];
                graph[parentNode][node] -= currentFlow;
                graph[node][parentNode] += currentFlow;

                node = parentNode;
            }
        }

        return flow;
    }

    int[][] graph;

    int[][] realgraph;

    public boolean test(double weight){
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                graph[i][j] = (int)(realgraph[i][j]/weight);
            }
        }
        return (getFlow(0,n-1)>=x);
    }
    int n,x;
    public void solution() throws IOException {
        // Number of nodes
        n = nextInt();
        realgraph = new int[n][n];
        graph = new int[n][n];

        //Number of edges.
        int m = nextInt();

        x = nextInt();

        // Directed flows. Source, Sink, Flow.
        for (int i = 0; i < m; i++) realgraph[nextInt()-1][nextInt()-1] = nextInt();

        double l = 0;
        double r = 1;
        while(test(r)){
            r*=2;
        }
        for(int i =0;i<100;i++){// 1e-6 precision approx 2^-19 precision.
            double mid = (l+r)/2;
            if(test(mid)){
                l = mid;
            }else{
                r = mid;
            }
        }
        println(l*x);


    }

    //Solution goes above: ------------------------------------
    public static final String IN_FILE = "D653.in";
    public static final String OUT_FILE = "";
    //-------------------- ------------------------------------
    //IO
    public static BufferedReader br;
    public static StringTokenizer st;
    public static BufferedWriter bw;

    public static void main(String[] args) throws IOException {
        if (IN_FILE == "") {
            br = new BufferedReader(new InputStreamReader(System.in));
        } else {
            try {
                br = new BufferedReader(new FileReader(IN_FILE));
            } catch (FileNotFoundException e) {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }
        if (OUT_FILE == "") {
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        } else {
            try {
                bw = new BufferedWriter(new FileWriter(OUT_FILE));
            } catch (FileNotFoundException e) {
                bw = new BufferedWriter(new OutputStreamWriter(System.out));
            }
        }
        (new D653()).solution();
        bw.close();//Flushes too.
    }

    public static String nextToken() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    public static String nextLine() {
        st = null;
        try {
            return br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }

    public static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    public static long nextLong() {
        return Long.parseLong(nextToken());
    }

    public static double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    public static void println(Object s) throws IOException {
        bw.write(s.toString() + "\n");
    }

    public static void println() throws IOException {
        bw.newLine();
    }

    public static void print(Object s) throws IOException {
        bw.write(s.toString());
    }

    public static void flush() throws IOException {//Useful for debug
        bw.flush();
    }

    //Other
    public static class Arr<T> extends ArrayList<T> {
    } //I hate typing ArrayList
}