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

from heapq import heappush, heappop
from collections import defaultdict, deque

def main():
  n, m = map(int, input().split())
  edges = [[] for _ in range(n)]
  cedges = defaultdict(lambda: [])
  for _ in range(m):
    p, q, c = map(int, input().split())
    edges[p-1].append((q-1, c))
    edges[q-1].append((p-1, c))
    cedges[p-1, c].append(q-1)
    cedges[q-1, c].append(p-1)

  ans = defaultdict(lambda: float('inf'))
  ans[0, -1] = 0  # ノード、路線
  que = deque([(0, 0, -1)])  # 距離、ノード、路線
  while len(que) > 0:
    d, u, c = que.popleft()
    if ans[u, c] < d:  # 更新しない
      continue
    if c < 0:
      for t, c2 in edges[u]:
        if d + 1 < ans[t, c2]:
          ans[t, c2] = d + 1
          que.append((d+1, t, c2))
    else:
      for t in cedges[u, c]:
        if d < ans[t, c]:
          ans[t, c] = d
          que.appendleft((d, t, c))
      if d < ans[u, -1]:
        ans[u, -1] = d
        que.appendleft((d, u, -1))
  try:
    print(min(d for (u, _), d in ans.items() if u == n-1))
  except ValueError:
    print(-1)


if __name__ == '__main__':
  main()