#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) FOR(i,0,n)
#define all(x) (x).begin(),(x).end()
#define PRINT(V) cout << V << "\n"
#define SORT(V) sort((V).begin(),(V).end())
#define RSORT(V) sort((V).rbegin(), (V).rend())
#define INF 1e8;
using namespace std;
using ll = long long;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

int V,E;
int to[17][17];
int dp[(1<<20)+1][17];

int dfs(){
    rep(i,(1<<V)){
        rep(j,V){
            if(!((1<<j)&i)){
                rep(k,V){
                    dp[i|(1<<j)][j] = min(dp[i|(1<<j)][j],dp[i][k]+to[k][j]);
                }
            }
        }
    }
    if(dp[(1<<V)-1][0] == 1e8) return -1;
    return dp[(1<<V)-1][0];
}
int main(){
    cin >> V >> E;
    rep(i,17) rep(j,17) to[i][j] = 1e8;
    rep(i,(1<<20)) rep(j,17) dp[i][j] = 1e8;
    int a,b,d;
    rep(i,E){
        cin >> a >> b >> d;
        to[a][b] = d;
    }
    dp[0][0] = 0;
    PRINT(dfs());
}


### 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 FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) FOR(i,0,n)
#define all(x) (x).begin(),(x).end()
#define PRINT(V) cout << V << "\n"
#define SORT(V) sort((V).begin(),(V).end())
#define RSORT(V) sort((V).rbegin(), (V).rend())
#define INF 1e8;
using namespace std;
using ll = long long;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

int V,E;
int to[17][17];
int dp[(1<<20)+1][17];

int dfs(){
    rep(i,(1<<V)){
        rep(j,V){
            if(!((1<<j)&i)){
                rep(k,V){
                    dp[i|(1<<j)][j] = min(dp[i|(1<<j)][j],dp[i][k]+to[k][j]);
                }
            }
        }
    }
    if(dp[(1<<V)-1][0] == 1e8) return -1;
    return dp[(1<<V)-1][0];
}
int main(){
    cin >> V >> E;
    rep(i,17) rep(j,17) to[i][j] = 1e8;
    rep(i,(1<<20)) rep(j,17) dp[i][j] = 1e8;
    int a,b,d;
    rep(i,E){
        cin >> a >> b >> d;
        to[a][b] = d;
    }
    dp[0][0] = 0;
    PRINT(dfs());
}


```