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\ndef input():\n\treturn sys.stdin.readline()[:-1]\n\nclass DijkstraList():\n\t#隣接リスト版\n\t#同一頂点の複数回探索を防ぐため訪問した頂点数を変数cntで持つ\n\tdef __init__(self, adj, start):\n\t\tself.list = adj\n\t\tself.start = start\n\t\tself.size = len(adj)\n\n\tdef solve(self):\n\t\t#self.dist = [float("inf") for _ in range(self.size)]\n\t\tself.dist = defaultdict(lambda :10**30)\n\t\tself.dist[self.start] = 0\n\t\t#self.prev = [-1 for _ in range(self.size)]\n\t\tself.q = []\n\t\tself.cnt = 0\n\n\t\theapq.heappush(self.q, (0, self.start))\n\n\t\twhile self.q and self.cnt < self.size:\n\t\t\tu_dist, u = heapq.heappop(self.q)\n\t\t\tif self.dist[u] < u_dist:\n\t\t\t\tcontinue\n\t\t\tfor v, w in self.list[u]:\n\t\t\t\tif self.dist[v] > u_dist + w:\n\t\t\t\t\tself.dist[v] = u_dist + w\n\t\t\t\t\t#self.prev[v] = u\n\t\t\t\t\theapq.heappush(self.q, (self.dist[v], v))\n\t\t\tself.cnt += 1\n\t\treturn\n\n\tdef distance(self, goal):\n\t\treturn self.dist[goal]\n\nn, m = map(int, input().split())\ncost = [10**30 for _ in range(n)]\nedges = defaultdict(list)\nfor _ in range(m):\n\tp, q, t = map(int, input().split())\n\tedges[p-1 + t * n].append((q-1 + t * n, 0))\n\tedges[q-1 + t * n].append((p-1 + t * n, 0))\n\tif len(edges[p-1 + t * n]) == 1:\n\t\tedges[p-1 + t * n].append((p-1 + 0 * n, 0))\n\t\tedges[p-1 + 0 * n].append((p-1 + t * n, 1))\n\tif len(edges[q-1 + t * n]) == 1:\n\t\tedges[q-1 + t * n].append((q-1 + 0 * n, 0))\n\t\tedges[q-1 + 0 * n].append((q-1 + t * n, 1))\n\nd = DijkstraList(edges, 0)\nd.solve()\nres = d.distance(n-1)\nif res > 10**20:\n\tprint(-1)\nelse:\n\tprint(res)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 18061