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 collections import *\nimport sys \nsys.setrecursionlimit(10 ** 9)\n\ndef solve():\n    def dfs(u, f):\n        G[u].append(f)\n        G1[f].append(u)\n        for v in g[u]:\n            if v not in used:\n                used.add(v)\n                dfs(v, f)\n\n    n, m = list(map(int, input().split()))\n    edges = []\n    for  _ in range(m):\n        edges.append(list(map(int, input().split())))\n    edges.sort(key = lambda item: item[2])\n    G = defaultdict(list)#记录每个点可能在哪个分组里面\n    G1 = defaultdict(list) #记录每个分组里面的点\n    en = 0\n    cnt = 0\n    while en < len(edges):\n        st = en \n        g = defaultdict(list)\n        used = set()\n        while en < len(edges) and edges[en][2] == edges[st][2]:\n            x, y = edges[en][0], edges[en][1]\n            g[x].append(y)\n            g[y].append(x)\n            en += 1\n        for k in g:\n            if k not in used:\n                used.add(k)\n                dfs(k, cnt)\n                cnt += 1\n    \n    usedG = set()\n    usedP = set()\n    deq = deque()\n    deq.append(1)\n    usedP.add(1)\n    step = 0\n    while deq:\n        siz = len(deq)\n        for _ in range(siz):\n            f = deq.popleft()\n            if f == n:\n                print(step)\n                return \n            for g in G[f]:\n                if g not in usedG:\n                    usedG.add(g)\n                    for p in G1[g]:\n                        if p not in usedP:\n                            usedP.add(p)\n                            deq.append(p)\n        step += 1\n    \n    print((-1))\n\nsolve()\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15967