#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int MAX_N = 15;
const int INF = 1<<29;

int main(int argc, char const *argv[])
{
    int n, e;
    int d[MAX_N][MAX_N];
    cin >> n >> e;

    for (int i = 0; i < n; ++i) {
        fill(d[i], d[i]+n, INF);
    }

    for (int i = 0; i < e; ++i) {
        int si, ti, di;
        cin >> si >> ti >> di;
        d[si][ti] = di;
    }

    int dp[1<<MAX_N][MAX_N];

    for (int i = 0; i < 1<<n; ++i) {
        fill(dp[i], dp[i]+n, INF);
    }

    dp[(1<<n)-1][0] = 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)) {
                    dp[s][v] = min(dp[s][v], dp[s | 1 << u][u] + d[v][u]);
                }
            }
        }
    }

    int ans;

    if (dp[0][0]<INF) {
        ans = dp[0][0];
    }
    else {
        ans = -1;
    }

    printf("%d\n", ans);


    return 0;
}

### Prompt

Please formulate 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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int MAX_N = 15;
const int INF = 1<<29;

int main(int argc, char const *argv[])
{
    int n, e;
    int d[MAX_N][MAX_N];
    cin >> n >> e;

    for (int i = 0; i < n; ++i) {
        fill(d[i], d[i]+n, INF);
    }

    for (int i = 0; i < e; ++i) {
        int si, ti, di;
        cin >> si >> ti >> di;
        d[si][ti] = di;
    }

    int dp[1<<MAX_N][MAX_N];

    for (int i = 0; i < 1<<n; ++i) {
        fill(dp[i], dp[i]+n, INF);
    }

    dp[(1<<n)-1][0] = 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)) {
                    dp[s][v] = min(dp[s][v], dp[s | 1 << u][u] + d[v][u]);
                }
            }
        }
    }

    int ans;

    if (dp[0][0]<INF) {
        ans = dp[0][0];
    }
    else {
        ans = -1;
    }

    printf("%d\n", ans);


    return 0;
}

```