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:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from collections import deque

N,M = map(int,readline().split())
if M == 0:
    print(-1)
    exit()
m = map(int,read().split())
P,Q,C = zip(*zip(m,m,m))

V = []
V += [p<<32 for p in range(1,N+1)]
V += [(p<<32)+c for p,c in zip(P,C)]
V += [(q<<32)+c for q,c in zip(Q,C)]
V = set(V)
label = {x:i for i,x in enumerate(V)}
start = label[1<<32]
goal = label[N<<32]

N = len(V)
graph = [[] for _ in range(N)]
for p,q,c in zip(P,Q,C):
    v0 = label[p<<32]; v1 = label[(p<<32)+c]
    w0 = label[q<<32]; w1 = label[(q<<32)+c]
    graph[v0].append((v1,1))
    graph[w0].append((w1,1))
    graph[v1].append((v0,0))
    graph[w1].append((w0,0))
    graph[v1].append((w1,0))
    graph[w1].append((v1,0))

INF = 10 ** 10
dist = [INF] * N
dist[start] = 0
q = deque([(0,start)])
while q:
    dv,v = q.popleft()
    for w,cost in graph[v]:
        dw = dv + cost
        if dw >= dist[w]:
            continue
        dist[w] = dw
        if not cost:
            q.appendleft((dw,w))
        else:
            q.append((dw,w))

answer = dist[goal]
if answer == INF:
    answer = -1
print(answer)