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 main():\n  from heapq import heappush,heappop,heapify\n  inf=2**31-1\n  n,m,*t=map(int,open(0).read().split())\n  z=[]\n  for a,b,c in zip(t[::3],t[1::3],t[2::3]):\n    z.extend([a,b,a+n*c,b+n*c])\n  z={i:v for v,i in enumerate(sorted(set(z)))}\n  try:\n    z[1]\n  except:\n    print(-1)\n    return\n  edge=[[]for _ in range(len(z))]\n  d={}\n  l=[]\n  for a,b,c in zip(t[::3],t[1::3],t[2::3]):\n    if b<a:a,b=b,a\n    i,j,x,y=z[a],z[b],z[a+n*c],z[b+n*c]\n    if b==n:\n      l.append(y)\n    edge[i].append((1,x))\n    edge[j].append((1,y))\n    edge[x].extend([(0,i),(0,y)])\n    edge[y].extend([(0,j),(0,x)])\n  used=[False]+[True]*~-len(z)\n  d=[0]+[inf]*~-len(z)\n  edgelist=edge[0]\n  heapify(edgelist)\n  while edgelist:\n    m=heappop(edgelist)\n    if not used[m[1]]:\n      continue\n    d[m[1]]=m[0]\n    used[m[1]]=False\n    for e in edge[m[1]]:\n      if used[e[1]]:\n        heappush(edgelist,(e[0]+m[0],e[1]))\n  a=min([d[i]for i in l]or[inf])\n  print([a,-1][a==inf])\ndef __starting_point():\n  main()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 20827