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 = "from collections import deque\nN, M = map(int, input().split())\nF_C_of_S = [{} for i in range(N)]\n#Companies of Station\nC_of_S = {}\n\n#def Union-find\nparent = [-1]*M\ndef root(x):\n\tif (parent[x] < 0): return x\n\telse:\n\t\tparent[x] = y = root(parent[x])\n\t\treturn y\n\ndef unite(x, y):\n\tpx = root(x)\n\tpy = root(y)\n\tif (px == py): return False\n\tif (parent[px] > parent[py]):\n\t\tpx = root(y)\n\t\tpy = root(x)\n\tparent[px] += parent[py]\n\tparent[py] = px\n\treturn True\n\n\n#Union-find\npqcs = []\nfor i in range(M):\n\tp, q, c = map(int, input().split())\n\tp -= 1; q -= 1;\n\tpqcs += [(p, q, c)]\n\t\n\t#The first\n\tif not c in F_C_of_S[p]: F_C_of_S[p][c] = i\n\t#else\n\telse: unite(F_C_of_S[p][c], i)\n\tC_of_S.setdefault(p, set()).add(c)\n\t\n\t#The first\n\tif not (c in F_C_of_S[q]):F_C_of_S[q][c] = i\n\t#else\n\telse: unite(F_C_of_S[q][c], i)\n\tC_of_S.setdefault(q, set()).add(c)\n\n#stations of company\nS_of_C = {}\nfor i in range(M):\n\tp, q, c = pqcs[i]\n\tc_set = S_of_C.setdefault(root(i), set())\n\tc_set.add(p)\n\tc_set.add(q)\n\n\nQ = deque([(0, 0, 0)])\n#cost to go to the stations from station_0\ndist = [float('inf')]*N\ndist[0] = 0\n\ngdist = [float('inf')]*M\n\nwhile Q:\n\tcost, v, flag = Q.popleft()\n\t\n\tif not (flag):#(flag == 0) then gdist_update\n\t\tif (dist[v] < cost) or (v not in C_of_S):\n\t\t\tcontinue\n\t\tfor l in F_C_of_S[v].values():\n\t\t\tl = root(l)\n\t\t\tif (cost < gdist[l]):\n\t\t\t\tgdist[l] = cost\n\t\t\t\tQ.appendleft((cost, l, 1))\n\t\n\telse:#(flag == 1) then dist_update\n\t\tif (gdist[v] < cost) or (v not in S_of_C):\n\t\t\tcontinue\n\t\tfor s in S_of_C[v]:\n\t\t\tif (cost+1 < dist[s]):\n\t\t\t\tdist[s] = cost+1\n\t\t\t\tQ.append((cost+1, s, 0))\n\nprint(dist[N - 1] if dist[N - 1] < float('inf') else -1)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14773