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 math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\neps = 1.0 / 10**10\nmod = 10**9+7\ndd = [(-1,0),(0,1),(1,0),(0,-1)]\nddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\ndef pf(s): return print(s, flush=True)\n\n\nclass UnionFind:\n    def __init__(self, size):\n        self.table = [-1 for _ in range(size)]\n\n    def find(self, x):\n        if self.table[x] < 0:\n            return x\n        else:\n            self.table[x] = self.find(self.table[x])\n            return self.table[x]\n\n    def union(self, x, y):\n        s1 = self.find(x)\n        s2 = self.find(y)\n        if s1 != s2:\n            if self.table[s1] <= self.table[s2]:\n                self.table[s1] += self.table[s2]\n                self.table[s2] = s1\n            else:\n                self.table[s2] += self.table[s1]\n                self.table[s1] = s2\n            return True\n        return False\n\n    def subsetall(self):\n        a = []\n        for i in range(len(self.table)):\n            if self.table[i] < 0:\n                a.append((i, -self.table[i]))\n        return a\n\n    def tall(self):\n        d = collections.defaultdict(list)\n        for i in range(len(self.table)):\n            d[self.find(i)].append(i)\n        return d\n\ndef main():\n    M = 2**17\n    n,m = LI()\n    a = [LI() for _ in range(m)]\n    e = collections.defaultdict(list)\n    for p,q,c in a:\n        pc = p+c*M\n        qc = q+c*M\n        pm = p-M\n        qm = q-M\n        e[pc].append(qc)\n        e[qc].append(pc)\n        e[pm].append(pc)\n        e[qm].append(qc)\n        e[pc].append(pm)\n        e[qc].append(qm)\n\n    def search():\n        d = collections.defaultdict(lambda: inf)\n        s = 1-M\n        d[s] = 0\n        q = []\n        heapq.heappush(q, (0, s))\n        v = set()\n        while len(q):\n            k, u = heapq.heappop(q)\n            if u in v:\n                continue\n            v.add(u)\n            if u < 0:\n                for uv in e[u]:\n                    if uv in v:\n                        continue\n                    vd = k + 1\n                    if d[uv] > vd:\n                        d[uv] = vd\n                        heapq.heappush(q, (vd, uv))\n\n            else:\n                if u % M == n:\n                    return k\n\n                for uv in e[u]:\n                    if uv in v:\n                        continue\n                    if d[uv] > k:\n                        d[uv] = k\n                        heapq.heappush(q, (k, uv))\n\n        return -1\n\n    return search()\n\n\n\nprint(main())\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 181563