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 = "#!/usr/bin python3\n# -*- coding: utf-8 -*-\n\n# https://atcoder.jp/contests/arc061/tasks/arc061_c\n\n########################################################\n# 01BFS\n########################################################\n\nfrom collections import deque\n\nn, m = list(map(int, input().split()))\nab = set([])\nps = set([i<<20 for i in range(1, n+1)])\n\nfor _ in range(m):\n    a, b, c = list(map(int, input().split()))\n    a <<= 20\n    b <<= 20\n    ps.add(a+c)\n    ps.add(b+c)\n    ab.add((a, b, c))\n\n\npsr = {ps:i for i, ps in enumerate(ps)}\npsc = len(ps)\ngmap = [[] for _ in range(psc)]\nfor a, b, c in ab:\n    a0 = psr[a]\n    b0 = psr[b]\n    a1 = psr[a+c]\n    b1 = psr[b+c]\n    gmap[a0].append((a1, 1))\n    gmap[b0].append((b1, 1))\n    gmap[a1].append((a0, 0))\n    gmap[b1].append((b0, 0))\n    gmap[a1].append((b1, 0))\n    gmap[b1].append((a1, 0))\n\nINF = float('inf')\ndist = [INF] * psc\n\ndef zero_one_bfs(sp, gp):\n    next_q = deque([])\n    next_q.append(sp)\n    dist[sp] = 0\n    while next_q:\n        cp = next_q.popleft()\n        cd = dist[cp]\n        if cp == gp: return cd\n        for np, pay in gmap[cp]:\n            if dist[np] <= cd+pay: continue\n            dist[np] = cd + pay\n            if pay == 1:\n                next_q.append(np)\n            else:\n                next_q.appendleft(np)\n    return dist[gp]\n\nret = zero_one_bfs(psr[1<<20], psr[n<<20])\nprint((-1 if ret == INF else ret))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14449