Snuke's Subway Trip

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

inputFormat

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

outputFormat

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

样例

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

2