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:
// package QS.AA.NetworkFlow;

// D. Delivery Bears
// https://codeforces.com/problemset/problem/653/D

// wrong answer

import java.io.*;
import java.util.*;
import java.util.stream.Stream;

public class CF_653D {
	
	public static final int MOD = 1000_000_000 + 7;
	public static final double EPS = 1e-9;
	public static final boolean DEBUG = false;

    static int n, m, k, en;
    static int[] q, dis, to, pre, c, last, cur;
    static Edge[] e;

    static void init() {
        q = new int[233];
        dis = new int[233];
        to = new int[2333];
        pre = new int[2333];
        c = new int[2333];
        last = new int[2333];
        cur = new int[2333];
        e = new Edge[550];
    }

    public static boolean check(double lim) {
        en = 1;
        Arrays.fill(last, 0);
        NetworkFlowSolverBase solver = new DinicsSolver(n + 1, 1, n);
    	for (int i = 1; i <= m; i++) {
            int capacity = (int)(e[i].capacity/lim);
    		if (capacity != 0) solver.addEdge( e[i].from, e[i].to, capacity);
    	}
    	long flow = solver.getMaxFlow();
    	return  flow >= k;
    } 

	public static void main(String[] args) throws java.io.IOException {
		final java.io.BufferedReader br = new java.io.BufferedReader(new java.io.InputStreamReader(System.in));
		final StringBuilder out = new StringBuilder();	
		String[] tokens = br.readLine().trim().split("\\s");
		n = Integer.parseInt(tokens[0]);
		m = Integer.parseInt(tokens[1]);
		k = Integer.parseInt(tokens[2]);
        init();
		double l = 0.0, r = 0.0, mid = 0.0;
		for (int i = 1; i <= m; i++) {
			tokens = br.readLine().trim().split("\\s");
			int u = Integer.parseInt(tokens[0]);
			int v = Integer.parseInt(tokens[1]);
			int w = Integer.parseInt(tokens[2]);
			e[i] = new Edge(u, v, w);
            r = Math.max(r, w);
		}

		while (r - l > EPS) {
			mid = l + (r - l) / 2;
			if (check(mid)) l = mid;
			else r = mid;
		}

		mid = mid * k;
		mid = Math.max(mid, 1);

        System.out.printf("%.7f\n", mid);
	}

    private static class Edge {
        public int from, to;
        public Edge residual;
        public long flow;
        public final long capacity;
        
        public Edge(int from, int to, long capacity) {
          this.from = from;
          this.to = to;
          this.capacity = capacity;
        }

        public boolean isResidual() {
          return capacity == 0;
        }

        public long remainingCapacity() {
          return capacity - flow;
        }

        public void augment(long bottleNeck) {
          flow += bottleNeck;
          residual.flow -= bottleNeck;
        }

        public String toString(int s, int t) {
          String u = (from == s) ? "s" : ((from == t) ? "t" : String.valueOf(from));
          String v = (to == s) ? "s" : ((to == t) ? "t" : String.valueOf(to));
          return String.format("Edge %s -> %s | flow = %3d | capacity = %3d | is residual: %s", 
            u, v, flow, capacity, isResidual());
        }
    }


    private static abstract class NetworkFlowSolverBase {
        static final long INF = Long.MAX_VALUE / 2;
        final int n, s, t;
        protected boolean solved;
        protected long maxFlow;
        protected List<Edge>[] graph;
        public NetworkFlowSolverBase(int n, int s, int t) {
          this.n = n; 
          this.s = s; 
          this.t = t; 
          initializeEmptyFlowGraph();
        }
        private void initializeEmptyFlowGraph() {
          graph = new List[n];
          for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<Edge>();
        }
        public void addEdge(int from, int to, long capacity) {
          if (capacity <= 0) 
            throw new IllegalArgumentException("Forward edge capacity <= 0");
          Edge e1 = new Edge(from, to, capacity);
          Edge e2 = new Edge(to, from, 0);
          e1.residual = e2;
          e2.residual = e1;
          graph[from].add(e1);
          graph[to].add(e2);
        }
        public List<Edge>[] getGraph() {
          execute();
          return graph;
        }
        public long getMaxFlow() {
          execute();
          return maxFlow;
        }
        private void execute() {
          if (solved) return; 
          solved = true;
          solve();
        }
        public abstract void solve();
    }
  
    private static class DinicsSolver extends NetworkFlowSolverBase {
        private int[] level;
        public DinicsSolver(int n, int s, int t) {
          super(n, s, t);
          level = new int[n];
        }

        @Override
        public void solve() {
         int[] next = new int[n];

          while (bfs()) {
            Arrays.fill(next, 0);
            for (long f = dfs(s, next, INF); f != 0; f = dfs(s, next, INF)) {
              maxFlow += f;
            }
          }
        }
        private boolean bfs() {
          Arrays.fill(level, -1);
          Deque<Integer> q = new ArrayDeque<>(n);
          q.offer(s);
          level[s] = 0;
          while (!q.isEmpty()) {
            int node = q.poll();
            for (Edge edge : graph[node]) {
              long cap = edge.remainingCapacity();
              if (cap > 0 && level[edge.to] == -1) {
                level[edge.to] = level[node] + 1;
                q.offer(edge.to);
              }
            }
          }
          return level[t] != -1;
        }
        private long dfs(int at, int[] next, long flow) {
          if (at == t) return flow;
          final int numEdges = graph[at].size();
          
          for (;next[at] < numEdges; next[at]++) {
            Edge edge = graph[at].get(next[at]);
            long cap = edge.remainingCapacity();
            if (cap > 0 && level[edge.to] == level[at] + 1) {

              long bottleNeck = dfs(edge.to, next, Math.min(flow, cap));
              if (bottleNeck > 0) {
                edge.augment(bottleNeck);
                return bottleNeck;
              }

            }
          }
          return 0;
        }
    }
}