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 = "# -*- coding: utf-8 -*-\nimport bisect\nimport heapq\nimport math\nimport random\nimport sys\nfrom collections import Counter, defaultdict, deque\nfrom decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal\nfrom functools import lru_cache, reduce\nfrom itertools import combinations, combinations_with_replacement, product, permutations\nfrom operator import add, mul, sub\n\nsys.setrecursionlimit(10000)\n\n\ndef read_int():\n    return int(input())\n\n\ndef read_int_n():\n    return list(map(int, input().split()))\n\n\ndef read_float():\n    return float(input())\n\n\ndef read_float_n():\n    return list(map(float, input().split()))\n\n\ndef read_str():\n    return input().strip()\n\n\ndef read_str_n():\n    return list(map(str, input().split()))\n\n\ndef error_print(*args):\n    print(*args, file=sys.stderr)\n\n\ndef mt(f):\n    import time\n\n    def wrap(*args, **kwargs):\n        s = time.time()\n        ret = f(*args, **kwargs)\n        e = time.time()\n\n        error_print(e - s, 'sec')\n        return ret\n\n    return wrap\n\n\ndef bfs01(g, s):\n    d = {}\n    for v in g.keys():\n        d[v] = sys.maxsize\n    d[s] = 0\n\n    if s not in d:\n        return d\n    q = deque()\n    q.append((d[s], s))\n\n    NM = 1 << 30\n    while q:\n        _, u = q.popleft()\n        for v in g[u]:\n            if v > NM:\n                c = 0\n            else:\n                c = 1\n            alt = c + d[u]\n            if d[v] > alt:\n                d[v] = alt\n                if c == 0:\n                    q.appendleft((d[v], v))\n                else:\n                    q.append((d[v], v))\n    return d\n\n\n@mt\ndef slv(N, M):\n\n    g = defaultdict(list)\n    NM = 30\n    for _ in range(M):\n        p, q, c = input().split()\n        p = int(p)\n        q = int(q)\n        c = int(c)\n\n        cp = (c << NM) + p\n        cq = (c << NM) + q\n        g[cp].append(cq)\n        g[cq].append(cp)\n        g[cp].append(p)\n        g[cq].append(q)\n        g[p].append((cp))\n        g[q].append((cq))\n\n    d = bfs01(g, 1)\n    return -1 if N not in d or d[N] == sys.maxsize else d[N]\n\n\ndef main():\n    N, M = read_int_n()\n\n    print(slv(N, M))\n\n\ndef __starting_point():\n    main()\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16405