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:
/*-
 * Codeforces problem :
 * http://codeforces.com/problemset/problem/653/D
 *
 * Find the max flow in a directed network with some constratints.
 */

import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.util.StringTokenizer;

/**
 * @author Karthik Venkataraman
 * @email kafy83@gmail.com
 */
public class DeliveryBears {

    private int n;
    private int m;
    private int x;
    private int[][] capacity;
    private int[][] testArr;
    private FixedList<Integer>[] adj;
    private int[] edgeTo;
    private boolean[] marked;
    private ResizingQueue<Integer> queue;

    class ResizingQueue<T> {

        private T[] items;
        private int last;
        private int first;
        private int size;

        ResizingQueue(int capacity) {
            this.items = (T[]) new Object[capacity];
        }

        void resize(int max) {
            T[] temp = (T[]) new Object[max];
            for (int i = 0; i < size; i++) {
                temp[i] = items[(first + i) % items.length];
            }
            items = temp;
            first = 0;
            last = size;
        }

        boolean isEmpty() {
            return size == 0;
        }

        void enqueue(T value) {
            if (size == items.length) {
                resize(2 * items.length);
            }
            items[last++] = value;
            if (last == items.length) {
                last = 0;
            }
            size++;
        }

        T dequeue() {
            T item = items[first];
            items[first] = null;
            size--;
            first++;
            if (first == items.length) {
                first = 0;
            }
            return item;
        }
    }

    class FixedList<T> implements Iterable<T> {

        class FixedListIterator<T> implements Iterator<T> {

            private int i = 0;

            @Override
            public boolean hasNext() {
                return i < size;
            }

            @Override
            public T next() {
                if (!hasNext()) {
                    throw new NoSuchElementException();
                }
                return (T) items[i++];
            }

        }
        private T[] items;
        private int size;

        FixedList(int capacity) {
            this.items = (T[]) new Object[capacity];
        }

        void add(T value) {
            items[size++] = value;
        }

        @Override
        public Iterator<T> iterator() {
            return new FixedListIterator();
        }
    }

    class InputReader {

        private static final int inputkb = 5 * 1024;
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), inputkb);
        }

        private String readNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException ex) {
                    throw new IllegalStateException(ex);
                }
            }
            return tokenizer.nextToken();
        }

        private int nextInt() {
            return Integer.parseInt(readNext());
        }
    }

    private boolean hasAugmentingPath() {
        marked = new boolean[n];
        edgeTo = new int[n];
        queue = new ResizingQueue<>(n);
        queue.enqueue(0);
        marked[0] = true;
        edgeTo[0] = -1;
        while (!queue.isEmpty() && !marked[n - 1]) {
            int v = queue.dequeue();
            for (int w : adj[v]) {
                if (testArr[v][w] > 0) {
                    if (!marked[w]) {
                        marked[w] = true;
                        edgeTo[w] = v;
                        queue.enqueue(w);
                    }
                }
            }
        }
        return marked[n - 1];
    }

    private long findMaxFlow() {
        long maxflow = 0;
        while (hasAugmentingPath()) {
            double bottle = Double.POSITIVE_INFINITY;
            for (int v = n - 1; v != 0; v = edgeTo[v]) {
                bottle = Math.min(bottle, testArr[edgeTo[v]][v]);
            }
            for (int v = n - 1; v != 0; v = edgeTo[v]) {
                testArr[edgeTo[v]][v] -= bottle;
                testArr[v][edgeTo[v]] += bottle;
            }
            maxflow += bottle;
        }
        return maxflow;
    }

    private void compute() {
        InputReader sc = new InputReader(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        x = sc.nextInt();
        capacity = new int[n][n];
        testArr = new int[n][n];
        adj = (FixedList<Integer>[]) new FixedList[n];
        for (int i = 0; i < n; i++) {
            adj[i] = new FixedList<>(n);
        }
        for (int i = 0; i < m; i++) {
            int from = sc.nextInt() - 1;
            int to = sc.nextInt() - 1;
            capacity[from][to] = sc.nextInt();
            adj[from].add(to);
        }

        double lo = 0, hi = 1e7;
        for (int iter = 0; iter < 100; iter++) {
            double mid = (lo + hi) / 2;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    testArr[i][j] = (int) (capacity[i][j] / mid);
                }
            }
            if (findMaxFlow() >= x) {
                lo = mid;
            } else {
                hi = mid;
            }
        }

        System.out.println(String.format("%.10f", lo * x));
    }

    public static void main(String[] args) {
        DeliveryBears db = new DeliveryBears();
        db.compute();
    }
}