subwaytrip

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: 123. 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: 13256. Then, use company 5's lines: 678. The fare is 2 yen.

Sample Input 3

2 0

Sample Output 3

-1

Submitting .cpp to 'subwaytrip'


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Compile Errors


							
Time Limit: 2 Seconds
Memory Limit: 1024MB
No. of ACs: 2
Your best score: 0
Source: Dunjudge Archive

Subtask Score
1 100
2 0