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/env python3\nimport sys\ninput = sys.stdin.readline\nfrom collections import deque\nINF = 10**9\n\nn, m = map(int, input().split())\npqc = []\n\nseen = set()\nfor i in range(n):\n    seen.add((i, 0))\nfor _ in range(m):\n    p, q, c = map(int, input().split())\n    p -= 1; q -= 1\n    pqc.append((p, q, c))\n    seen.add((p, c))\n    seen.add((q, c))\ncomp = dict()\nfor i, node in enumerate(seen):\n    comp[node] = i\n\nedge = [[] for _ in range(len(comp))]\nfor key in comp.keys():\n    v, c = key\n    if c != 0:\n        frm = comp[(v, c)]\n        too = comp[(v, 0)]\n        edge[frm].append((too, 0))\n        edge[too].append((frm, 1))\n\nfor p, q, c in pqc:\n    frm = comp[(p, c)]\n    too = comp[(q, c)]\n    edge[frm].append((too, 0))\n    edge[too].append((frm, 0))\n\nclass BFS:\n    def __init__(self, adj):\n        self.adj = adj\n        self.dist = [INF] * len(adj)\n        self.q = deque()\n\n    def calc(self, start):\n        self.dist[start] = 0\n        self.q.append((0, start))\n        while len(self.q) != 0:\n            prov_cost, src = self.q.popleft()\n            if self.dist[src] < prov_cost:\n                continue\n            for dest, cost in self.adj[src]:\n                if self.dist[dest] > self.dist[src] + cost:\n                    self.dist[dest] = self.dist[src] + cost\n                    if cost == 1:\n                        self.q.append((self.dist[dest], dest))\n                    else:\n                        self.q.appendleft((self.dist[dest], dest))\n        return self.dist\n\nbfs = BFS(edge)\nbfs.calc(comp[(0, 0)])\nans = bfs.dist[comp[(n-1, 0)]]\nif ans == INF:\n    print(-1)\nelse:\n    print(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15517