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>
using namespace std;
int adjMat[16][16];
bool visited[16][1 << 16];
int dp[16][1 << 16];
int v, e;
const char *byte_to_binary(int x) {
  static char b[9];
  b[0] = '\0';
  int z;
  for (z = 128; z > 0; z >>= 1) {
    strcat(b, ((x & z) == z) ? "1" : "0");
  }
  return b;
}
int TSP(int at, int state) {
  if (state == (1 << v) - 1) {
    visited[at][state] = true;
    return dp[at][state];
  }
  if (dp[at][state]) return dp[at][state];
  int ans = INT_MAX >> 1;
  int cost;
  for (int i = 0; i < v; i++) {
    if (adjMat[at][i] != -1 && (state & (1 << i)) == 0) {
      cost = TSP(i, state | (1 << i)) + adjMat[at][i];
      ans = min(ans, cost);
    }
  }
  return dp[at][state] = ans;
}
int main() {
  while (~scanf("%d %d", &v, &e)) {
    memset(adjMat, -1, sizeof(adjMat));
    for (int i = 0; i < e; i++) {
      int u, v, w;
      scanf("%d%d%d", &u, &v, &w);
      adjMat[u][v] = w;
    }
    memset(dp, 0, sizeof(dp));
    memset(visited, 0, sizeof(visited));
    int ans = TSP(0, 0);
    if (ans >= INT_MAX >> 1)
      puts("-1");
    else
      printf("%d\n", ans);
  }
  return 0;
}
