#include <bits/stdc++.h>
using namespace std;
#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
#define all(x) (x).begin(),(x).end()
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
typedef long long ll;
const long long INF = 1LL << 60;
typedef pair<int, int> P;

int main()
{
    int v, e;
    cin >> v >> e;

    vector<vector<int>> dis(v, vector<int>(v, 1e9));
    rep(i, e) {
        int s, t, d;
        cin >> s >> t >> d;
        dis[s][t] = d;
    }

    vector<vector<int>> dp((1 << v), vector<int>(v, 1e9));

    rep(i, v) dp[0][0] = 0;
    rep(s, 1 << v) {
        rep(now, v) {
            rep(to, v) {
                if ((s >> to) & 1 || dis[now][to] == 1e9) continue;
                chmin(dp[s|(1 << to)][to], dp[s][now] + dis[now][to]);
            }
        }
    }

    int ans = dp[(1 << v) - 1][0];
    cout << (ans == 1e9 ? -1 : ans) << endl;
    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 <bits/stdc++.h>
using namespace std;
#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
#define all(x) (x).begin(),(x).end()
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
typedef long long ll;
const long long INF = 1LL << 60;
typedef pair<int, int> P;

int main()
{
    int v, e;
    cin >> v >> e;

    vector<vector<int>> dis(v, vector<int>(v, 1e9));
    rep(i, e) {
        int s, t, d;
        cin >> s >> t >> d;
        dis[s][t] = d;
    }

    vector<vector<int>> dp((1 << v), vector<int>(v, 1e9));

    rep(i, v) dp[0][0] = 0;
    rep(s, 1 << v) {
        rep(now, v) {
            rep(to, v) {
                if ((s >> to) & 1 || dis[now][to] == 1e9) continue;
                chmin(dp[s|(1 << to)][to], dp[s][now] + dis[now][to]);
            }
        }
    }

    int ans = dp[(1 << v) - 1][0];
    cout << (ans == 1e9 ? -1 : ans) << endl;
    return 0;
}

```