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 = 'from sys import setrecursionlimit, stderr\nfrom functools import reduce\nfrom itertools import *\nfrom collections import *\nfrom bisect import bisect\nfrom heapq import *\n\ndef read():\n  return int(input())\n \ndef reads():\n  return [int(x) for x in input().split()]\n\nN, M = reads()\nedges = [[] for _ in range(N)]\nedgesc = defaultdict(lambda: [])\nfor _ in range(M):\n  p, q, c = reads()\n  p, q = p-1, q-1\n  edges[p].append((q, c))\n  edges[q].append((p, c))\n  edgesc[p, c].append(q)\n  edgesc[q, c].append(p)\n\nINF = 1 << 30\ndef dijkstra(edges, s):\n  result = defaultdict(lambda: INF)\n  result[s, -1] = 0\n  que = deque([(0, s, -1)])\n  while len(que) > 0:\n    (d, u, c) = que.popleft()\n    if result[u, c] < d:\n      continue\n    if c < 0:\n      for (t, c2) in edges[u]:\n        if d + 1 < result[t, c2]:\n          result[t, c2] = d + 1\n          que.append((d + 1, t, c2))\n    else:\n      for t in edgesc[u, c]:\n        if d < result[t, c]:\n          result[t, c] = d\n          que.appendleft((d, t, c))\n      if d < result[u, -1]:\n        result[u, -1] = d\n        que.appendleft((d, u, -1))\n  return result\n\ndist = dijkstra(edges, 0)\ntry:\n  print(min(d for (u, _), d in dist.items() if u == N-1))\nexcept ValueError:\n  print(-1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17581