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:
from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import *
from bisect import bisect
from heapq import *

def read():
  return int(input())
 
def reads():
  return [int(x) for x in input().split()]

N, M = reads()
edges = [[] for _ in range(N)]
edgesc = defaultdict(lambda: [])
for _ in range(M):
  p, q, c = reads()
  p, q = p-1, q-1
  edges[p].append((q, c))
  edges[q].append((p, c))
  edgesc[p, c].append(q)
  edgesc[q, c].append(p)

INF = 1 << 30
def dijkstra(edges, s):
  result = defaultdict(lambda: INF)
  result[s, -1] = 0
  que = deque([(0, s, -1)])
  while len(que) > 0:
    (d, u, c) = que.popleft()
    if result[u, c] < d:
      continue
    if c < 0:
      for (t, c2) in edges[u]:
        if d + 1 < result[t, c2]:
          result[t, c2] = d + 1
          que.append((d + 1, t, c2))
    else:
      for t in edgesc[u, c]:
        if d < result[t, c]:
          result[t, c] = d
          que.appendleft((d, t, c))
      if d < result[u, -1]:
        result[u, -1] = d
        que.appendleft((d, u, -1))
  return result

dist = dijkstra(edges, 0)
try:
  print(min(d for (u, _), d in dist.items() if u == N-1))
except ValueError:
  print(-1)