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 = 'N, M = list(map(int, input().split()))\nES = []\nD = {}\n\n*parent, = list(range(M))\ndef root(x):\n    if x == parent[x]:\n        return x\n    parent[x] = y = root(parent[x])\n    return y\ndef unite(x, y):\n    px = root(x); py = root(y)\n    if px < py:\n        parent[py] = px\n    else:\n        parent[px] = py\n\nE = {}\nfor i in range(M):\n    p, q, c = list(map(int, input().split())); p -= 1; q -= 1\n    ES.append((p, q, c))\n    if (p, c) in D:\n        unite(D[p, c], i)\n    D[p, c] = i\n    E.setdefault(p, set()).add(c)\n    if (q, c) in D:\n        unite(D[q, c], i)\n    D[q, c] = i\n    E.setdefault(q, set()).add(c)\n#P = [[] for i in range(M)]\nP = {}\nfor i in range(M):\n    j = root(i)\n    p, q, c = ES[i]\n    s = P.setdefault(j, set())\n    s.add(p); s.add(q)\n\nfrom collections import deque\nque = deque([(0, 0, 0)])\nINF = 10**18\ndist = [INF]*N\ndist[0] = 0\ngdist = [INF]*M\n\nwhile que:\n    cost, v, t = que.popleft()\n    if t:\n        # edge\n        if gdist[v] < cost or v not in P:\n            continue\n        for w in P[v]:\n            if cost + 1 < dist[w]:\n                dist[w] = cost + 1\n                que.append((cost + 1, w, 0))\n    else:\n        # node\n        if dist[v] < cost or v not in E:\n            continue\n        for c in E[v]:\n            w = root(D[v, c])\n            if cost < gdist[w]:\n                gdist[w] = cost\n                que.appendleft((cost, w, 1))\n\nprint((dist[N-1] if dist[N-1] < INF else -1))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14195