For a given weighted directed graph G(V, E), find the distance of the shortest route that meets the following criteria:

* It is a closed cycle where it ends at the same point it starts.
* It visits each vertex exactly once.

Constraints

* 2 ≤ |V| ≤ 15
* 0 ≤ di ≤ 1,000
* There are no multiedge

Input


|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target vertices of i-th edge (directed) and di represents the distance between si and ti (the i-th edge).

Output

Print the shortest distance in a line. If there is no solution, print -1.

Examples

Input

4 6
0 1 2
1 2 3
1 3 9
2 0 1
2 3 6
3 2 4


Output

16


Input

3 3
0 1 1
1 2 1
0 2 1


Output

-1
import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

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

public class Main {
    static int MOD = 1000000007;

    // public static class Mas {
    // int x;
    // int y;
    // int step;

    // Mas(int x, int y, int step) {
    // this.x = x;
    // this.y = y;
    // this.step = step;
    // }
    // }

    static long pow(long l, long i) {
        if (i == 0)
            return 1;
        else {
            if (i % 2 == 0) {
                long val = pow(l, i / 2);
                return val * val % 2019;
            } else {
                return pow(l, i - 1) * l % 2019;
            }
        }
    }

    private static final int[] vX = { 1, 0, 0, -1 };
    private static final int[] vY = { 0, 1, -1, 0 };
    static int V, E;
    static int[][] G = new int[20][20]; // グラフ
    static int[][] dp = new int[50000][20];

    static int rec(int S, int v) {
        if (S == 0) {
            if (v == 0) {
                return 0;
            } else {
                return 100000000;
            }
        }
        if ((S & (1 << v)) == 0) { // Sに{v}が含まれていない
            return 100000000;
        }

        int ret = dp[S][v];
        if (ret != 0)
            return ret;

        ret = 100000000;
        for (int i = 0; i < V; i++) {
            ret = Math.min(ret, rec(S ^ (1 << v), i)) + G[i][v];
        }
        return ret;
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();

        V = fs.nextInt();
        E = fs.nextInt();
        for (int i = 0; i < 20; i++) {
            for (int j = 0; j < 20; j++) {
                G[i][j] = 100000000;
            }
        }
        for (int i = 0; i < E; i++) {
            int s = fs.nextInt();
            int t = fs.nextInt();
            int d = fs.nextInt();
            G[s][t] = d;
        }
        for (int i = 0; i < 50000; i++) {
            for (int j = 0; j < 20; j++) {
                dp[i][j] = 100000000;
            }
        }
        dp[0][0] = 0;
        for (int i = 0; i < (1 << V); i++) {
            for (int j = 0; j < V; j++) {
                for (int k = 0; k < V; k++) {
                    if ((i & (1 << j)) == 0) {
                        if (j != k)
                            dp[i | (1 << j)][j] = Math.min(dp[i | (1 << j)][j], dp[i][k] + G[k][j]);
                    }
                }
            }
        }
        if (dp[(1 << V) - 1][0] != 100000000) {
            System.out.println(dp[(1 << V) - 1][0]);
        } else {
            System.out.println(-1);
        }
    }
}

