Title
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 ≤ i ≤ M ) line connects station pi and qi bidirectionally. There is no intermediate station. This line is operated by company ci.
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 ≤ N ≤ 105
- 0 ≤ M ≤ 2×105
- 1 ≤ pi ≤ N (1 ≤ i ≤ M)
- 1 ≤ qi ≤ N (1 ≤ i ≤ M)
- 1 ≤ ci ≤ 106 (1 ≤ i ≤ M)
- pi ≠ qi (1 ≤ i ≤ M)
Input
The input is given from Standard Input in the following format:
N M
p1 q1 c1
:
pM qM cM
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