#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
template<class T> bool chmin(T &a, T b) {if(a>b) {a=b;return 1;}return 0;}
using namespace std;
using ll = long long;
const int inf = 1e8;

int main() {
    int n, e;
    cin >> n >> e;
    int dp[1<<n][n];
    vector<vector<int>> d(n,vector<int>(n,-1));
    rep(i,e) {
        int s, t, cost;
        cin >> s >> t >> cost;
        d[s][t] = cost;
    }
    int ans = inf;
    rep(V,n) {
        rep(i,1<<n)rep(j,n) dp[i][j] = inf;
        dp[(1<<n)-1][V] = 0;
        for (int S = (1<<n) - 2; S >= 0; S--) {
            for (int v = 0; v < n; v++) {
                for (int u = 0; u < n; u++) {
                    if (!(S >> u & 1) && (d[v][u] != -1)) {
                        dp[S][v] = min(dp[S][v],dp[S|1<<u][u] + d[v][u]);
                    }
                }
            }
        }
        ans = min(ans,dp[0][V]);
    }
    if (ans == inf) cout << -1 << endl;
    else cout << ans << endl;
}

### Prompt

Your task is to create a CPP solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
template<class T> bool chmin(T &a, T b) {if(a>b) {a=b;return 1;}return 0;}
using namespace std;
using ll = long long;
const int inf = 1e8;

int main() {
    int n, e;
    cin >> n >> e;
    int dp[1<<n][n];
    vector<vector<int>> d(n,vector<int>(n,-1));
    rep(i,e) {
        int s, t, cost;
        cin >> s >> t >> cost;
        d[s][t] = cost;
    }
    int ans = inf;
    rep(V,n) {
        rep(i,1<<n)rep(j,n) dp[i][j] = inf;
        dp[(1<<n)-1][V] = 0;
        for (int S = (1<<n) - 2; S >= 0; S--) {
            for (int v = 0; v < n; v++) {
                for (int u = 0; u < n; u++) {
                    if (!(S >> u & 1) && (d[v][u] != -1)) {
                        dp[S][v] = min(dp[S][v],dp[S|1<<u][u] + d[v][u]);
                    }
                }
            }
        }
        ans = min(ans,dp[0][V]);
    }
    if (ans == inf) cout << -1 << endl;
    else cout << ans << endl;
}

```