#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <cmath>
#include <algorithm>
#include <iomanip>
#include <queue>
#include <tuple>
using ll = long long;
using namespace std;

int d[15][15];
int dp[1 << 15][15];
int main(void)
{
    int V, E;
    cin >> V >> E;
    for (int i = 0; i < V; ++i)
        for (int j = 0; j < V; ++j)
            d[i][j] = 1e8;
    for (int i = 0; i < E; ++i)
    {
        int s, t, ds;
        cin >> s >> t >> ds;
        d[s][t] = ds;
    }

    for (int S = 0; S < 1 << V; ++S)
    {
        for (int i = 0; i < V; ++i)
        {
            dp[S][i] = 1e8;
        }
    }

    dp[(1 << V) - 1][0] = 0;

    for (int S = (1 << V) - 2; S >= 0; S--)
    {
        for (int v = 0; v < V; ++v)
        {
            for (int u = 0; u < V; ++u)
            {
                if (!(S >> u & 1))
                {
                    dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + d[v][u]);
                }
            }
        }
    }
    if (dp[0][0] != 1e8)
        cout << dp[0][0] << endl;
    else
        cout << -1 << endl;
    return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 <iostream>
#include <string>
#include <vector>
#include <set>
#include <cmath>
#include <algorithm>
#include <iomanip>
#include <queue>
#include <tuple>
using ll = long long;
using namespace std;

int d[15][15];
int dp[1 << 15][15];
int main(void)
{
    int V, E;
    cin >> V >> E;
    for (int i = 0; i < V; ++i)
        for (int j = 0; j < V; ++j)
            d[i][j] = 1e8;
    for (int i = 0; i < E; ++i)
    {
        int s, t, ds;
        cin >> s >> t >> ds;
        d[s][t] = ds;
    }

    for (int S = 0; S < 1 << V; ++S)
    {
        for (int i = 0; i < V; ++i)
        {
            dp[S][i] = 1e8;
        }
    }

    dp[(1 << V) - 1][0] = 0;

    for (int S = (1 << V) - 2; S >= 0; S--)
    {
        for (int v = 0; v < V; ++v)
        {
            for (int u = 0; u < V; ++u)
            {
                if (!(S >> u & 1))
                {
                    dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + d[v][u]);
                }
            }
        }
    }
    if (dp[0][0] != 1e8)
        cout << dp[0][0] << endl;
    else
        cout << -1 << endl;
    return 0;
}

```