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 sys,heapq\nfrom collections import defaultdict,deque\n\ninput = sys.stdin.readline\nn,m = map(int,input().split())\n#+路線*chg : その路線ホーム\nchg = 10**6\n\nedge=defaultdict(set)\nused =defaultdict(bool)\nfor i in range(m):\n    p,q,c = map(int,input().split())\n    edge[p].add(p+c*chg)\n    edge[p+c*chg].add(p)\n    edge[p+c*chg].add(q+c*chg)\n    edge[q+c*chg].add(p+c*chg)\n    edge[q].add(q+c*chg)\n    edge[q+c*chg].add(q)\n    used[p] = False\n    used[q] = False\n    used[p+c*chg] = False\n    used[q+c*chg] = False\n\nedgelist = deque()\nedgelist.append((1,0))\nres = float("inf")\n\nwhile len(edgelist):\n    x,cost = edgelist.pop()\n    used[x] = True\n\n    if x == n:\n        res = cost\n        break\n    for e in edge[x]:\n        if used[e]:\n            continue\n        #ホーム→改札\n        if x <= 10**5 and chg <= e:\n            edgelist.appendleft((e,cost+1))\n        else:\n            edgelist.append((e,cost))\n        \nif res == float("inf"):\n    print(-1)\nelse:\n    print(res)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14559