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

struct Problem {

    UL D[15][15];
    UL dp[1 << 15][15];

    void Solve() {
        UL N, M; scanf("%d%d", &N, &M);
        rep(i, N) rep(j, N) D[i][j] = 1000000;
        rep(i, M) {
            UL u, v, d; scanf("%d%d%d", &u, &v, &d);
            D[u][v] = d;
        }
        rep(i, 1 << N) rep(j, N) dp[i][j] = 1000000;
        dp[0][0] = 0;
        rep(i, 1 << N) {
            rep(j, N) {
                rep(k, N) {
                    if (i & 1 << k) continue;
                    dp[i | (1 << k)][k] = min(dp[i | (1 << k)][k], dp[i][j] + D[j][k]);
                }
            }
        }
        if (dp[(1 << N) - 1][0] >= 1000000) printf("-1\n");
        else printf("%d\n", dp[(1 << N) - 1][0]);
    }
};
int main() {
    unique_ptr<Problem> p(new Problem());
    p->Solve();
    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;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

    UL D[15][15];
    UL dp[1 << 15][15];

    void Solve() {
        UL N, M; scanf("%d%d", &N, &M);
        rep(i, N) rep(j, N) D[i][j] = 1000000;
        rep(i, M) {
            UL u, v, d; scanf("%d%d%d", &u, &v, &d);
            D[u][v] = d;
        }
        rep(i, 1 << N) rep(j, N) dp[i][j] = 1000000;
        dp[0][0] = 0;
        rep(i, 1 << N) {
            rep(j, N) {
                rep(k, N) {
                    if (i & 1 << k) continue;
                    dp[i | (1 << k)][k] = min(dp[i | (1 << k)][k], dp[i][j] + D[j][k]);
                }
            }
        }
        if (dp[(1 << N) - 1][0] >= 1000000) printf("-1\n");
        else printf("%d\n", dp[(1 << N) - 1][0]);
    }
};
int main() {
    unique_ptr<Problem> p(new Problem());
    p->Solve();
    return 0;
}


```