Problem:
Score : 600 points

Problem Statement

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 1

3 3
1 2 1
2 3 1
3 1 2

Sample Output 1

1

Use company 1's lines: 1 → 2 → 3. The fare is 1 yen.

Sample Input 2

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

Sample Output 2

2

First, use company 1's lines: 1 → 3 → 2 → 5 → 6. Then, use company 5's lines: 6 → 7 → 8. The fare is 2 yen.

Sample Input 3

2 0

Sample Output 3

-1

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N, M = gets.split.map(&:to_i)
edges = Array.new(N+1){{}}
companies = Array.new(N+1){{}}
M.times do
    p, q, c = gets.split.map(&:to_i)
    edges[p][c] ||= []
    edges[p][c].push(q)
    edges[q][c] ||= []
    edges[q][c].push(p)
    companies[p][c] = true
    companies[q][c] = true
end

dist = {}
deque = edges[1].keys.map{|c| c*(N+1) + 1}
deque.each do |code|
    dist[code] = 1
end
while deque.length > 0
    a = deque.shift
    ca = a / (N+1)
    na = a % (N+1)
    edges[na][ca].each do |nb|
        if nb == N
            puts dist[a]
            exit
        end
        b = ca * (N+1) + nb
        if !dist[b] || dist[b] > dist[a]
            dist[b] = dist[a]
            deque.unshift(b)
        end
    end
    companies[na].each do |c, _|
        aa = c * (N+1) + na
        if !dist[aa] || dist[aa] > dist[a] + 1
            dist[aa] = dist[a] + 1
            deque.push(aa)
        end
    end
end
puts -1