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
#!/usr/bin/env python3
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

v,e=map(int,input().split())
G=[[] for i in range(v)]
for i in range(e):
    s,t,d=map(int,input().split())
    G[s].append((t,d))
dp=[[inf]*v for i in range(2**v)]
dp[1][0]=0
for bit in range(1,2**v):
    for i in range(v):
        if dp[bit][i]==inf: continue
        for gi,di in G[i]:
            if not (bit >> gi & 1):
                dp[bit|1<<gi][gi]=min(dp[bit|1<<gi][gi],dp[bit][i]+di)
            if bit == (1 << v) - 1 and gi == 0:
                dp[bit][0] = min (dp[bit][0],dp[bit][i]+di)
print(dp[2**v-1][0] if dp[2**v-1][0]!=inf else -1)
# print(*dp,sep="\n")
# print(*G,sep="\n")
