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;
inline bool ChekBit(int mask, int index) { return (bool)((mask >> index) & 1); }
inline int UpDateMask(int mask, int index) { return mask | (1 << index); }
inline unsigned int Min(unsigned int a, unsigned int b) {
  if (a < b && a != 0)
    return a;
  else {
    return b;
  }
}
int main() {
  int n;
  int m;
  ifstream file("input.txt");
  cin >> n;
  cin >> m;
  vector<vector<pair<int, int>>> map(n);
  vector<int> weightToEnd(n, -1);
  for (int i = 0; i < m; i++) {
    int vertuxStart;
    int vertuxEnd;
    int weight;
    cin >> vertuxStart;
    cin >> vertuxEnd;
    cin >> weight;
    map[vertuxStart].push_back(make_pair(vertuxEnd, weight));
    if (vertuxEnd == 0) {
      weightToEnd[vertuxStart] = weight;
    }
  }
  file.close();
  int exp = (int)pow(2, n);
  vector<vector<unsigned int>> dState = vector<vector<unsigned int>>(
      exp, vector<unsigned int>(n, (unsigned int)-1));
  dState[1][0] = 0;
  for (int mask = 1; mask < exp; mask++) {
    for (int vertexCurrent = 0; vertexCurrent < n; ++vertexCurrent) {
      if (!ChekBit(mask, vertexCurrent)) {
        continue;
      }
      if (dState[mask][vertexCurrent] == (unsigned int)-1) {
        continue;
      }
      for (size_t i = 0; i < map[vertexCurrent].size(); ++i) {
        int vertexEnd = map[vertexCurrent][i].first;
        int weight = map[vertexCurrent][i].second;
        if (!ChekBit(mask, vertexEnd)) {
          int tmpMask = UpDateMask(mask, vertexEnd);
          dState[tmpMask][vertexEnd] = Min(
              dState[tmpMask][vertexEnd], dState[mask][vertexCurrent] + weight);
        }
      }
    }
  }
  unsigned int answer = (unsigned int)-1;
  for (int i = 0; i < n; i++) {
    if (weightToEnd[i] == -1) {
      continue;
    }
    if (dState[exp - 1][i] == (unsigned int)-1) {
      continue;
    }
    answer = Min(answer, dState[exp - 1][i] + weightToEnd[i]);
  }
  cout << (int)answer << endl;
  return 0;
}
