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 = 'def dijkstra_heap(s,edge,mask):\n    dist = defaultdict(lambda: float("inf"))\n    q = [s]  # 0 が会社に属していない状態\n    dist[s] = 0\n    d = 0; q0 = []; q1 = []\n    while q:\n        for x in q:\n            if x & mask == 0:\n                for y in edge[x]:\n                    if dist[y[1]] <= d + y[0]:\n                        continue\n                    dist[y[1]] = d + y[0]\n                    q1.append(y[1])\n            else:\n                for y in edge[x]:\n                    if dist[y[1]] <= d+ y[0]:\n                        continue\n                    dist[y[1]] = d+ y[0]\n                    q0.append(y[1])\n        if q0:\n            q = q0\n            q0 = []\n            continue\n        q = q1\n        q1 = []\n        d += 1\n    return dist\n\ndef examE(inf):\n    N, M = LI()\n    edge = defaultdict(list)\n    # edge[i] : iから出る道の[重み,行先]の配列\n    L = 32\n    Mask = (1 << L) - 1\n    for i in range(M):\n        p, q, c = list(map(int, input().split()))\n        p -=1; q -=1\n        p <<= L\n        q <<= L\n        #同じ路線だとコスト０ 乗るときだけコスト１\n        edge[p].append((1,p + c))\n        edge[p + c].append((0,p))\n        edge[q].append((1,q + c))\n        edge[q + c].append((0,q))\n        edge[p + c].append((0,q + c))\n        edge[q + c].append((0,p + c))\n    start = 0\n    goal = (N-1) << L\n    res = dijkstra_heap(start, edge, Mask)\n#    print(res)\n    ans = res[goal]\n    if ans == inf:\n        ans = -1\n    print(ans)\n\n\nimport sys,copy,bisect,itertools,heapq,math\nfrom heapq import heappop,heappush,heapify\nfrom collections import Counter,defaultdict,deque\ndef I(): return int(sys.stdin.readline())\ndef LI(): return list(map(int,sys.stdin.readline().split()))\ndef LS(): return sys.stdin.readline().split()\ndef S(): return sys.stdin.readline().strip()\nmod = 10**9 + 7\ninf = float(\'inf\')\n\nexamE(inf)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 178429