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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const long long MAX_V = 15;
const long long INF = 1LL<<60;

vector<vector<long long>> G(MAX_V, vector<long long>(1<<MAX_V, INF));
vector<vector<long long>> dist(MAX_V, vector<long long>(MAX_V, INF));

int main(){
    
    int V, E;
    cin >> V >> E;
    
    for (int i = 0; i < E; i++){
        long long s, t, d;
        cin >> s >> t >> d;
        
        dist[s][t] = d;
    }
    
    G[0][1] = 0;
    
    //
    for (int s = 0; s < (1<<V); s++){
        
        for (int from = 0; from < V; from++){
            
            for (int to = 0; to < V; to++){
                
                if (!(s & (1<<from))) continue;
                if (s & (1<<to)) continue;
                
                G[to][s | (1<<to)] = min(G[to][s | (1<<to)], G[from][s] + dist[from][to]);
            }
        }
    }
    
    long long ans = INF;
    
    for (int i = 1; i < V; i++){
        ans = min(ans, G[i][(1<<V)-1] + dist[i][0]);
    }
    
    if (ans == INF) cout << -1 << endl;
    else cout << ans << endl;
    return 0;
     
}

