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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Alex
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }
    static class TaskD {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int nodes = in.readInt(); // n [2, 50]
            int edges = in.readInt(); // m [1, 500]
            int bears = in.readInt(); // x [1, 100_000]
            int[] a = new int[edges], b = new int[edges], c = new int[edges];
            IOUtils.readIntArrays(in, a, b, c);
            MiscUtils.decreaseByOne(a, b);
            double low = 0, high = 1000001;
            for(int iter = 0; iter < 100; iter++) {
                double mid = (low + high) / 2;
                Graph g = new Graph(nodes);
                for(int edge = 0; edge < edges; edge++) {
                    int units = (int) (c[edge] / mid);
                    g.addFlowEdge(a[edge], b[edge], units);
                }
                long res = MaxFlow.dinic(g, 0, nodes - 1);
                if(res >= bears) low = mid;
                else high = mid;
            }
            out.printLine(low * bears);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if(numChars == -1)
                throw new InputMismatchException();
            if(curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch(IOException e) {
                    throw new InputMismatchException();
                }
                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while(isSpaceChar(c))
                c = read();
            int sgn = 1;
            if(c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if(c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while(!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if(filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static interface IntCollection extends IntStream {
        public int size();

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

        default public void add(int value) {
            throw new UnsupportedOperationException();
        }

        default public IntCollection addAll(IntStream values) {
            for(IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static interface Edge {
    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static class MaxFlow {
        private final Graph graph;
        private int source;
        private int destination;
        private IntQueue queue;
        private int[] distance;
        private int[] nextEdge;

        public MaxFlow(Graph graph, int source, int destination) {
            this.graph = graph;
            this.source = source;
            this.destination = destination;
            int vertexCount = graph.vertexCount();
            queue = new IntArrayQueue(vertexCount);
            distance = new int[vertexCount];
            nextEdge = new int[vertexCount];
        }

        public static long dinic(Graph graph, int source, int destination) {
            return new MaxFlow(graph, source, destination).dinic();
        }

        public long dinic() {
            long totalFlow = 0;
            while(true) {
                edgeDistances();
                if(distance[destination] == -1)
                    break;
                Arrays.fill(nextEdge, -2);
                totalFlow += dinicImpl(source, Long.MAX_VALUE);
            }
            return totalFlow;
        }

        private void edgeDistances() {
            Arrays.fill(distance, -1);
            distance[source] = 0;
            queue.add(source);
            while(!queue.isEmpty()) {
                int current = queue.poll();
                int id = graph.firstOutbound(current);
                while(id != -1) {
                    if(graph.capacity(id) != 0) {
                        int next = graph.destination(id);
                        if(distance[next] == -1) {
                            distance[next] = distance[current] + 1;
                            queue.add(next);
                        }
                    }
                    id = graph.nextOutbound(id);
                }
            }
        }

        private long dinicImpl(int source, long flow) {
            if(source == destination)
                return flow;
            if(flow == 0 || distance[source] == distance[destination])
                return 0;
            int id = nextEdge[source];
            if(id == -2)
                nextEdge[source] = id = graph.firstOutbound(source);
            long totalPushed = 0;
            while(id != -1) {
                int nextDestinationID = graph.destination(id);
                if(graph.capacity(id) != 0 && distance[nextDestinationID] == distance[source] + 1) {
                    long pushed = dinicImpl(nextDestinationID, Math.min(flow, graph.capacity(id)));
                    if(pushed != 0) {
                        graph.pushFlow(id, pushed);
                        flow -= pushed;
                        totalPushed += pushed;
                        if(flow == 0)
                            return totalPushed;
                    }
                }
                nextEdge[source] = id = graph.nextOutbound(id);
            }
            return totalPushed;
        }

    }

    static class MiscUtils {
        public static void decreaseByOne(int[]... arrays) {
            for(int[] array : arrays) {
                for(int i = 0; i < array.length; i++)
                    array[i]--;
            }
        }

    }

    static class Graph {
        public static final int REMOVED_BIT = 0;
        protected int vertexCount;
        protected int edgeCount;
        private int[] firstOutbound;
        private int[] firstInbound;
        private Edge[] edges;
        private int[] nextInbound;
        private int[] nextOutbound;
        private int[] from;
        private int[] to;
        private long[] weight;
        public long[] capacity;
        private int[] reverseEdge;
        private int[] flags;

        public Graph(int vertexCount) {
            this(vertexCount, vertexCount);
        }

        public Graph(int vertexCount, int edgeCapacity) {
            this.vertexCount = vertexCount;
            firstOutbound = new int[vertexCount];
            Arrays.fill(firstOutbound, -1);

            from = new int[edgeCapacity];
            to = new int[edgeCapacity];
            nextOutbound = new int[edgeCapacity];
            flags = new int[edgeCapacity];
        }

        public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge) {
            ensureEdgeCapacity(edgeCount + 1);
            if(firstOutbound[fromID] != -1)
                nextOutbound[edgeCount] = firstOutbound[fromID];
            else
                nextOutbound[edgeCount] = -1;
            firstOutbound[fromID] = edgeCount;
            if(firstInbound != null) {
                if(firstInbound[toID] != -1)
                    nextInbound[edgeCount] = firstInbound[toID];
                else
                    nextInbound[edgeCount] = -1;
                firstInbound[toID] = edgeCount;
            }
            this.from[edgeCount] = fromID;
            this.to[edgeCount] = toID;
            if(capacity != 0) {
                if(this.capacity == null)
                    this.capacity = new long[from.length];
                this.capacity[edgeCount] = capacity;
            }
            if(weight != 0) {
                if(this.weight == null)
                    this.weight = new long[from.length];
                this.weight[edgeCount] = weight;
            }
            if(reverseEdge != -1) {
                if(this.reverseEdge == null) {
                    this.reverseEdge = new int[from.length];
                    Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
                }
                this.reverseEdge[edgeCount] = reverseEdge;
            }
            if(edges != null)
                edges[edgeCount] = createEdge(edgeCount);
            return edgeCount++;
        }

        protected final GraphEdge createEdge(int id) {
            return new GraphEdge(id);
        }

        public final int addFlowWeightedEdge(int from, int to, long weight, long capacity) {
            if(capacity == 0) {
                return addEdge(from, to, weight, 0, -1);
            } else {
                int lastEdgeCount = edgeCount;
                addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
                return addEdge(from, to, weight, capacity, lastEdgeCount);
            }
        }

        protected int entriesPerEdge() {
            return 1;
        }

        public final int addFlowEdge(int from, int to, long capacity) {
            return addFlowWeightedEdge(from, to, 0, capacity);
        }

        public final int vertexCount() {
            return vertexCount;
        }

        public final int firstOutbound(int vertex) {
            int id = firstOutbound[vertex];
            while(id != -1 && isRemoved(id))
                id = nextOutbound[id];
            return id;
        }

        public final int nextOutbound(int id) {
            id = nextOutbound[id];
            while(id != -1 && isRemoved(id))
                id = nextOutbound[id];
            return id;
        }

        public final int destination(int id) {
            return to[id];
        }

        public final long capacity(int id) {
            if(capacity == null)
                return 0;
            return capacity[id];
        }

        public final long flow(int id) {
            if(reverseEdge == null)
                return 0;
            return capacity[reverseEdge[id]];
        }

        public final void pushFlow(int id, long flow) {
            if(flow == 0)
                return;
            if(flow > 0) {
                if(capacity(id) < flow)
                    throw new IllegalArgumentException("Not enough capacity");
            } else {
                if(flow(id) < -flow)
                    throw new IllegalArgumentException("Not enough capacity");
            }
            capacity[id] -= flow;
            capacity[reverseEdge[id]] += flow;
        }

        public final boolean flag(int id, int bit) {
            return (flags[id] >> bit & 1) != 0;
        }

        public final boolean isRemoved(int id) {
            return flag(id, REMOVED_BIT);
        }

        protected void ensureEdgeCapacity(int size) {
            if(from.length < size) {
                int newSize = Math.max(size, 2 * from.length);
                if(edges != null)
                    edges = resize(edges, newSize);
                from = resize(from, newSize);
                to = resize(to, newSize);
                nextOutbound = resize(nextOutbound, newSize);
                if(nextInbound != null)
                    nextInbound = resize(nextInbound, newSize);
                if(weight != null)
                    weight = resize(weight, newSize);
                if(capacity != null)
                    capacity = resize(capacity, newSize);
                if(reverseEdge != null)
                    reverseEdge = resize(reverseEdge, newSize);
                flags = resize(flags, newSize);
            }
        }

        protected final int[] resize(int[] array, int size) {
            int[] newArray = new int[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        private long[] resize(long[] array, int size) {
            long[] newArray = new long[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        private Edge[] resize(Edge[] array, int size) {
            Edge[] newArray = new Edge[size];
            System.arraycopy(array, 0, newArray, 0, array.length);
            return newArray;
        }

        protected class GraphEdge implements Edge {
            protected int id;

            protected GraphEdge(int id) {
                this.id = id;
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for(int i = 0; i < objects.length; i++) {
                if(i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class IntArrayQueue implements IntQueue {
        private int[] data;
        private int from;
        private int to;

        public IntArrayQueue(int capacity) {
            data = new int[Integer.highestOneBit(capacity) << 1];
        }

        public IntArrayQueue() {
            this(3);
        }

        public IntArrayQueue(int[] array) {
            this(array.length);
            to = array.length;
            System.arraycopy(array, 0, data, 0, to);
        }

        public IntArrayQueue(IntStream s) {
            addAll(s);
        }

        public IntArrayQueue(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public int size() {
            return (to - from) & (data.length - 1);
        }

        public void add(int v) {
            ensureCapacity(size() + 1);
            data[to++] = v;
            to &= data.length - 1;
        }

        public int poll() {
            if(from == to) {
                throw new NoSuchElementException();
            }
            int result = data[from++];
            from &= data.length - 1;
            return result;
        }

        public IntIterator intIterator() {
            return new IntIterator() {
                private int at = from;

                public int value() {
                    if(at == to) {
                        throw new NoSuchElementException();
                    }
                    return data[at];
                }

                public boolean advance() {
                    if(!isValid()) {
                        throw new NoSuchElementException();
                    }
                    at++;
                    at &= data.length - 1;
                    return isValid();
                }

                public boolean isValid() {
                    return at != to;
                }

                public void remove() {
                    throw new UnsupportedOperationException();
                }
            };
        }

        private void ensureCapacity(int capacity) {
            if(data.length <= capacity) {
                int[] newData = new int[Integer.highestOneBit(capacity) << 1];
                if(from <= to) {
                    System.arraycopy(data, from, newData, 0, size());
                } else {
                    System.arraycopy(data, from, newData, 0, data.length - from);
                    System.arraycopy(data, 0, newData, data.length - from, to);
                }
                to = size();
                from = 0;
                data = newData;
            }
        }

    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        public IntIterator intIterator();

        default public Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default public int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while(it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if(i < j) {
                    return -1;
                } else if(i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if(it.isValid()) {
                return 1;
            }
            if(jt.isValid()) {
                return -1;
            }
            return 0;
        }

    }

    static class IOUtils {
        public static void readIntArrays(InputReader in, int[]... arrays) {
            for(int i = 0; i < arrays[0].length; i++) {
                for(int j = 0; j < arrays.length; j++)
                    arrays[j][i] = in.readInt();
            }
        }

    }

    static interface IntQueue extends IntCollection {
        public int poll();

    }
}