#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i=0; i < (int)(n); i++)
using ull = unsigned long long;
using ll = long long;

const int INF = 1E+9;

int V, E;
struct city{
    int t;
    int d;
};
vector<vector<city>> G(16);

int dp[1<<16][16];

int main() {
    cin >> V >> E;

    int si, ti, di;
    rep(i, E) {
        cin >> si >> ti >> di;
        G[si].push_back({ti, di});
    }

    rep(i, 1<<16) rep(j, 16) dp[i][j] = INF;
    dp[0][0] = 0;

    for (int bit=0; bit < (1<<V); bit++) {
        for (int now=0; now<V; now++) {
            for (auto c: G[now]) {
                if (!(bit & (1<<c.t))) {
                    dp[bit | (1<<c.t)][c.t] = min(dp[bit | (1<<c.t)][c.t], dp[bit][now] + c.d);
                }
            }
        }
    }

    int ans = dp[(1<<V)-1][0];
    if (ans == INF) ans = -1;
    cout << ans << endl;

    return 0;
}



### 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>
using namespace std;
#define rep(i, n) for (int i=0; i < (int)(n); i++)
using ull = unsigned long long;
using ll = long long;

const int INF = 1E+9;

int V, E;
struct city{
    int t;
    int d;
};
vector<vector<city>> G(16);

int dp[1<<16][16];

int main() {
    cin >> V >> E;

    int si, ti, di;
    rep(i, E) {
        cin >> si >> ti >> di;
        G[si].push_back({ti, di});
    }

    rep(i, 1<<16) rep(j, 16) dp[i][j] = INF;
    dp[0][0] = 0;

    for (int bit=0; bit < (1<<V); bit++) {
        for (int now=0; now<V; now++) {
            for (auto c: G[now]) {
                if (!(bit & (1<<c.t))) {
                    dp[bit | (1<<c.t)][c.t] = min(dp[bit | (1<<c.t)][c.t], dp[bit][now] + c.d);
                }
            }
        }
    }

    int ans = dp[(1<<V)-1][0];
    if (ans == INF) ans = -1;
    cout << ans << endl;

    return 0;
}



```