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 defaultdict, deque\n\nN, M = list(map(int, input().split()))\nD = {}\nEdges = []\n\n\nclass UnionFind:\n    def __init__(self, n):\n        self.par = [i for i in range(n)]\n        self.rank = [0] * n\n\n    # 検索\n    def find(self, x):\n        if self.par[x] == x:\n            return x\n        else:\n            self.par[x] = self.find(self.par[x])\n            return self.par[x]\n\n    # 併合\n    def union(self, x, y):\n        x = self.find(x)\n        y = self.find(y)\n\n        if x == y:\n            return\n\n        if self.rank[x] < self.rank[y]:\n            self.par[x] = y\n        else:\n            self.par[y] = x\n            if self.rank[x] == self.rank[y]:\n                self.rank[x] += 1\n\n    # すべての頂点に対して親を検索する\n    def all_find(self):\n        for n in range(len(self.par)):\n            self.find(n)\n\n\nUF = UnionFind(M)\nfor i in range(M):\n    p, q, c = list(map(int, input().split()))\n    p, q = p-1, q-1\n    Edges.append((p, q))\n\n    if (p, c) in D:\n        UF.union(D[p, c], i)\n    D[p, c] = i\n\n    if (q, c) in D:\n        UF.union(D[q, c], i)\n    D[q, c] = i\n\nUF.all_find()\n\nFirm_Node = defaultdict(set)\nfor i in range(M):\n    p, q = Edges[i]\n    Firm_Node[UF.par[i]].add(p)\n    Firm_Node[UF.par[i]].add(q)\n\nG = defaultdict(list)\nfor firm, node in list(Firm_Node.items()):\n    for n in node:\n        G[n].append(firm + N)\n        G[firm + N].append(n)\n\n\ndef dijkstra(x):\n    d = {x: 0, N-1: 10**9}\n    visited = {x}\n\n    # d, u\n    queue = deque([(0, x)])\n\n    while queue:\n        u = queue.pop()[1]\n        visited.add(u)\n\n        for node in G[u]:\n            d.setdefault(node, float('inf'))\n            if (node not in visited) and d[node] > d[u] + 1:\n                d[node] = d[u] + 1\n                if d[N-1] < 10**9:\n                    return d\n                queue.appendleft([d[u]+1, node])\n    return d\n\n\ndist = dijkstra(0)\nprint((dist[N-1] // 2 if dist[N-1] < 2*M else -1))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15639