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 = '# https://juppy.hatenablog.com/entry/2019/04/10/ARC061_-_E_%E3%81%99%E3%81%AC%E3%81%91%E5%90%9B%E3%81%AE%E5%9C%B0%E4%B8%8B%E9%89%84%E6%97%85%E8%A1%8C_-_Python_%E7%AB%B6%E6%8A%80%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0_Atcoder\n# 参考にさせていただきました。\n\nfrom collections import deque, defaultdict\n\nchg = 10**6\nn, m = map(int, input().split())\nedges = defaultdict(set)\n# m=0のためにdefaultdictにしておくべき\nvisited = defaultdict(set)\nfor i in range(m):\n    p, q, c = map(int, input().split())\n    edges[p+c*chg].add(q+c*chg)\n    edges[q+c*chg].add(p+c*chg)\n    edges[p].add(p+c*chg)\n    edges[q].add(q+c*chg)\n    edges[p+c*chg].add(p)\n    edges[q+c*chg].add(q)\n    visited[p] = False\n    visited[q] = False\n    visited[p+c*chg] = False\n    visited[q+c*chg] = False\n\nans = float("inf")\nque = deque()\n# now, dist\nque.append((1, 0))\n# 今求めるのはendの距離だけなので、dist配列はいらない\n# さらに、距離は0/1なのでheapで辺を管理する必要もなく、0なら最短確定なので先に、1ならその時点での最長なので後ろにすれば良い\nwhile que:\n    now, dist = que.popleft()\n    if visited[now]:\n        continue\n    visited[now] = True\n    if now == n:\n        ans = dist\n        break\n    for to in edges[now]:\n        # 駅→ホーム\n        if now < chg and to > chg:\n            que.append((to, dist+1))\n        else:\n            que.appendleft((to, dist))\nif ans == float("inf"):\n    print(-1)\nelse:\n    print(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14411