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
input = sys.stdin.readline
sys.setrecursionlimit(10**9)
from collections import deque, defaultdict
N, M = map(int, input().split())
G = defaultdict(list)
for _ in range(M):
    p, q, c = map(int, input().split())
    G[(p-1, c-1)].append((p-1, -1))
    G[(q-1, c-1)].append((q-1, -1))
    G[(p-1, -1)].append((p-1, c-1))
    G[(q-1, -1)].append((q-1, c-1))
    G[(p-1, c-1)].append((q-1, c-1))
    G[(q-1, c-1)].append((p-1, c-1))


dist = defaultdict(lambda :-1)
que = deque([(0, -1)])
dist[(0, -1)] = 0
while que:
    v = que.pop()
    d = dist[v]
    for nv in G[v]:
        if dist[nv]<0:
            if nv[1] == -1:
                dist[nv] = d+1
                que.appendleft(nv)
            else:
                dist[nv] = d
                que.append(nv)
print(dist[(N-1, -1)])