Problem: Snuke's town has a subway system, consisting of N stations and M railway lines. The stations are numbered 1 through N. Each line is operated by a company. Each company has an identification number.

The i-th ( 1 \leq i \leq M ) line connects station p_i and q_i bidirectionally. There is no intermediate station. This line is operated by company c_i.

You can change trains at a station where multiple lines are available.

The fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is 1 yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of 1 yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.

Snuke is now at station 1 and wants to travel to station N by subway. Find the minimum required fare.

Constraints

* 2 \leq N \leq 10^5
* 0 \leq M \leq 2×10^5
* 1 \leq p_i \leq N (1 \leq i \leq M)
* 1 \leq q_i \leq N (1 \leq i \leq M)
* 1 \leq c_i \leq 10^6 (1 \leq i \leq M)
* p_i \neq q_i (1 \leq i \leq M)

Input

The input is given from Standard Input in the following format:


N M
p_1 q_1 c_1
:
p_M q_M c_M


Output

Print the minimum required fare. If it is impossible to get to station N by subway, print `-1` instead.

Examples

Input

3 3
1 2 1
2 3 1
3 1 2


Output

1


Input

8 11
1 3 1
1 4 2
2 3 1
2 5 1
3 4 3
3 6 3
3 7 3
4 8 4
5 6 1
6 7 5
7 8 5


Output

2


Input

2 0


Output

-1

Solution (in PYTHON3):

Solution:
import sys
from collections import defaultdict,deque

def main():
    input = sys.stdin.readline
    n,m = map(int,input().split())
    #+路線*chg : その路線ホーム
    chg = 10**6

    edge=defaultdict(set)
    used =defaultdict(bool)
    for i in range(m):
        p,q,c = map(int,input().split())
        edge[p].add(p+c*chg)
        edge[p+c*chg].add(p)
        edge[p+c*chg].add(q+c*chg)
        edge[q+c*chg].add(p+c*chg)
        edge[q].add(q+c*chg)
        edge[q+c*chg].add(q)
        used[p] = False
        used[q] = False
        used[p+c*chg] = False
        used[q+c*chg] = False

    edgelist = deque()
    edgelist.append((1,0))
    res = float("inf")
    while len(edgelist):
        x,cost = edgelist.pop()
        used[x] = True

        if x == n:
            res = cost
            break
        for e in edge[x]:
            if used[e]:
                continue
            #行先が改札
            if x <= 10**5 and chg <= e:
                edgelist.appendleft((e,cost+1))
            else:
                edgelist.append((e,cost))
            
    if res == float("inf"):
        print(-1)
    else:
        print(res)
if __name__ == '__main__':
    main()