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 = 'import sys\ninput = sys.stdin.readline\nfrom collections import defaultdict\n\n"""\n(駅、会社)を頂点にグラフを持つ。頂点数O(M)。\nそのまま辺を貼ると辺が多くなりすぎる。\n(駅、会社) -> (駅、無属性) -> (駅、会社)\n"""\n\nL = 32\nmask = (1 << L) - 1\nN,M = map(int,input().split())\ngraph = defaultdict(list)\nfor _ in range(M):\n    p,q,c = map(int,input().split())\n    p <<= L\n    q <<= L\n    graph[p].append(p+c)\n    graph[p+c].append(p)\n    graph[q].append(q+c)\n    graph[q+c].append(q)\n    graph[p+c].append(q+c)\n    graph[q+c].append(p+c)\n\nINF = 10 ** 9\ndist = defaultdict(lambda: INF)\n\nstart = 1 << L\ngoal = N << L\n\nq = [start] # 0 が会社に属していない状態\ndist[start] = 0\nd = 0\nq0 = []\nq1 = []\nwhile q:\n    for x in q:\n        if x & mask == 0:\n            for y in graph[x]:\n                if dist[y] <= d + 1:\n                    continue\n                dist[y] = d + 1\n                q1.append(y)\n        else:\n            for y in graph[x]:\n                if dist[y] <= d:\n                    continue\n                dist[y] = d\n                q0.append(y)\n    if q0:\n        q = q0\n        q0 = []\n        continue\n    q = q1\n    q1 = []\n    d += 1\n\nanswer = dist[goal]\nif answer == INF:\n    answer = -1\nprint(answer)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14447