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 std.stdio, std.string, std.conv, std.algorithm, std.array;

enum VMAX = 15 + 1;
enum INF = 1 << 29;

int[VMAX][VMAX] table;
int[1<<VMAX][VMAX] dp;
int V, E;

int solve(int S, int v) {
    if ( dp[v][S] >= 0 ) {
        return dp[v][S];
    }

    if ( S == (1 << V) - 1 && v == 0 ) {
        return dp[v][S] = 0;
    }

    int tmp = INF;
    for( int u=0; u<V; ++u ) {
        if ( !( S >> u & 1 ) ) {
            // goto u from v
            tmp = min(tmp, solve(S | 1 << u, u) + table[u][v]);
        }
    }

    return dp[v][S] = tmp;
}

void main() {
    fill(table[0..$][0..$], INF);

    immutable ss = readln.chomp.split(" ").map!(to!int).array;
    V = ss[0];
    E = ss[1];

    for( int i=0; i<E; ++i ) {
        immutable sss = readln.chomp.split(" ").map!(to!int).array;
        immutable start = sss[0], end = sss[1], cost = sss[2];
        table[end][start] = cost;
    }


    fill(dp[0..$][0..$], -1);

    solve(0, 0).writeln;

}