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
#include<bits/stdc++.h>
const int INF = 1001001001;
using namespace std;
///////////////////////////////////////
struct edge {
	int to, cost;
	edge(int a, int b) :to(a), cost(b) {}
};
int n, m;
vector<edge>G[15];
int dp[1 << 16][15];
int solve(int s) {
	fill_n(*dp, (1 << 16) * 15, INF);
	dp[0][s] = 0;
	for (int i = 0; i < (1 << n); ++i) {
		for (int j = 0; j < n; ++j) {
			if (dp[i][j] == INF)continue;
			for (int k = 0; k < G[j].size(); ++k) {
				edge  &e = G[j][k];
				if (i>>e.to&1)continue;
				dp[i | (1 << e.to)][e.to] = min(dp[i | (1 << e.to)][e.to], dp[i][j] + e.cost);
			}
		}
	}
	return dp[(1 << n) - 1][s];
}
int main() {
	cin >> n >> m;
	for (int i = 0; i < m; ++i) {
		int a, b, c; cin >> a >> b >> c;
		G[a].push_back(edge(b,c));
	}
	int mi = INF;
	for (int i = 0; i < n; ++i)mi = min(mi, solve(i));
	if (mi == INF)cout << -1 << endl;
	else cout << mi << endl;
	return 0;
}
