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.

-----Sample Input-----
3 3
1 2 1
2 3 1
3 1 2

-----Sample Output-----
1

Use company 1's lines: 1 → 2 → 3. The fare is 1 yen.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def main():\n  N,M=map(int,input().split())\n\n  if M == 0:\n    print(-1)\n    return\n\n  INF = 10**6\n  pqc = [tuple(map(lambda x:int(x)-1,input().split())) for _ in range(M)]\n\n  to1d={v:{} for v in range(N)}\n  count=2\n  for p,q,c in pqc:\n    if not to1d[p].get(c):\n      to1d[p][c] = count\n      count += 1\n    if not to1d[q].get(c):\n      to1d[q][c] = count\n      count += 1\n\n  G = [{} for _ in range(N+count)]\n  for p,q,c in pqc:\n    v1,v2 = to1d[p][c],to1d[q][c]\n    G[v1][v2] = G[v2][v1] = 0\n\n  for i in range(N):\n    if len(to1d[i])<=1: continue\n    for c in to1d[i].keys():\n      v = to1d[i][c]\n      G[v][count] = 1\n      G[count][v] = 0\n    count += 1\n\n  def dijkstra(start = 0, goal = 1):\n      from heapq import heappop, heappush\n      NN = len(G)\n      d = [INF]*NN\n      d[start] = 0\n      que = []\n      heappush(que, start)\n      while que:\n          p = divmod(heappop(que),NN)\n          v = p[1]\n          if d[v] < p[0]: continue\n          for u in G[v].keys():\n              if d[u] > d[v] + G[v][u]:\n                  d[u] = d[v] + G[v][u]\n                  heappush(que, d[u]*NN+u)\n          if v == goal: return d[goal]\n      return d[goal]\n\n  for c in to1d[0].keys():\n    v = to1d[0][c]\n    G[0][v] = 1\n  for c in to1d[N-1].keys():\n    v = to1d[N-1][c]\n    G[v][1] = 0\n\n  ans = dijkstra(0,1)\n  print(ans if ans < INF else -1)\n  \ndef __starting_point():\n  main()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14773