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 heapq\n\nINF = 1000000000\n\n\ndef dijkstra(G, d, s):\n    h = []\n    d[s] = 0\n    heapq.heappush(h, (0, s))\n\n    while len(h) != 0:\n        p = heapq.heappop(h)\n        v = p[1]\n        if d[v] < p[0]:\n            continue\n        for e in G[v]:\n            if d[e[0]] > d[v] + e[1]:\n                d[e[0]] = d[v] + e[1]\n                heapq.heappush(h, (d[e[0]], e[0]))\n\n\ndef main():\n    N, M = list(map(int, input().split()))\n    p = [0] * M\n    q = [0] * M\n    c = [0] * M\n    for i in range(M):\n        p[i], q[i], c[i] = list(map(int, input().split()))\n        p[i] -= 1\n        q[i] -= 1\n    plat = []\n    for i in range(N):\n        plat.append(dict())\n    v_count = 0\n    for i in range(M):\n        p1 = plat[p[i]]\n        if not c[i] in p1:\n            p1[c[i]] = v_count\n            v_count += 1\n        p2 = plat[q[i]]\n        if not c[i] in p2:\n            p2[c[i]] = v_count\n            v_count += 1\n    for i in range(N):\n        plat[i][-1] = v_count\n        v_count += 1\n\n    G = [[] for _ in range(v_count)]\n    for i in range(M):\n        p1 = plat[p[i]][c[i]]\n        q1 = plat[q[i]][c[i]]\n        G[p1].append((q1, 0))\n        G[q1].append((p1, 0))\n    for i in range(N):\n        out = plat[i][-1]\n        for v in list(plat[i].values()):\n            if v == -1:\n                continue\n            G[v].append((out, 0))\n            G[out].append((v, 1))\n\n    start = plat[0][-1]\n    goal = plat[N - 1][-1]\n\n    d = [INF for _ in range(v_count)]\n\n    dijkstra(G, d, start)\n\n    if d[goal] == INF:\n        print((-1))\n    else:\n        print((d[goal]))\n\n\ndef __starting_point():\n    main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15363