Problem: 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.

Examples

Input

3 3
1 2 1
2 3 1
3 1 2


Output

1


Input

8 11
1 3 1
1 4 2
2 3 1
2 5 1
3 4 3
3 6 3
3 7 3
4 8 4
5 6 1
6 7 5
7 8 5


Output

2


Input

2 0


Output

-1

Solution (in PYTHON3):

Solution:
from heapq import heappush, heappop, heapify
import sys
input = sys.stdin.buffer.readline

N, M = map(int, input().split())
C = set()

edges = [[] for _ in range(N)]
for _ in range(M):
    fr, to, c = map(int, input().split())
    fr -= 1
    to -= 1
    edges[fr].append((to, c))
    edges[to].append((fr, c))
    C.add(c)

minDist = [10**18] * (N + 1)
minDistList = [set() for _ in range(N)]
minDistList[0] = C

que = [(1, 0, 0)]
while que:
    dist, f, now = heappop(que)

    for to, c in edges[now]:
        d = dist
        if not c in minDistList[now]:
            d += 1
        if minDist[to] > d:
            minDist[to] = d
            minDistList[to] = set()
            heappush(que, (d, f + 1, to))
        if minDist[to] == d:
            minDistList[to].add(c)

for _ in range(2):
    que = [(minDist[i], 0, i) for i in range(N)]
    heapify(que)
    while que:
        dist, f, now = heappop(que)

        for to, c in edges[now]:
            d = dist
            if not c in minDistList[now]:
                d += 1
            if minDist[to] > d:
                minDist[to] = d
                minDistList[to] = set()
                heappush(que, (d, f + 1, to))
            if minDist[to] == d:
                minDistList[to].add(c)

ans = minDist[N - 1]
print(ans if ans < 10**18 else -1)