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
stdin = sys.stdin
 
sys.setrecursionlimit(10**5) 
 
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

from collections import defaultdict, deque

# 入力・隣接リスト作成
n,m = li()
graph = defaultdict(set)
geta = pow(10,7)

for _ in range(m):
    p,q,c = li()
    
    graph[p + c*geta].add(q + c*geta)
    graph[q + c*geta].add(p + c*geta)
    
    graph[p + c*geta].add(p)
    graph[q + c*geta].add(q)
    
    graph[p].add(p + c*geta)
    graph[q].add(q + c*geta)
    
que = deque()
que.append((0, 1))
visited = set()

ans = -1

while que:
    (cost, node) = que.popleft()
    
    if node in visited:
        continue
    
    elif node % geta == n:
        ans = cost
        break
    
    visited.add(node)
    
    
    for nex in graph[node]:
        if nex in visited:
            continue
        
        elif node <= n and nex > n:
            que.append((cost+1, nex))
            
        else:
            que.appendleft((cost, nex))
    
print(ans)