In recent years space travel has become significantly cheaper. With this advancement in technology, space transit has become a booming business, and you just got hired as the logistics coordinator!

You have been provided with a list of ~N~ nearby planets, each with a unique integer id \(a_i\space(a_i>0)\).

Each planet ~a_i~ is also supplemented with a list of all \(M\space(0\le M\le N)\) planets, with unique integer ids \(m_i\space(m_i>0)\), that a spaceship could reach with one tank of gas.

You have been tasked with writing a program to find the minimum number of stops ~D~ that a spaceship needs to make in order to transport a client from their starting planet ~A~ to their destination planet ~B~.

If the trip is not possible, output -1

Input Specification

The first line of input contains two space separated integers, ~A~ and ~B~.

The next line of input contains the number of nearby planets ~N~.

The following ~N~ lines contain an integer ~a_i~, followed by an integer ~M~, followed by ~M~ integers ~m_i~.

Output Specification

Output one integer ~D~, the minimum number of stops required, or -1.

Constraints

Subtask 1 [40%]

~1\le N\le 500~

Subtask 2 [60%]

~1\le N\le 10^4~

Sample Input

1 4
4
1 1 2
2 3 1 3 4
3 2 2 4
4 2 2 3

Sample Output

1

Sample Explanation

In this case, the spaceship starts at planet 1 and refuels at planet 2 in order to make it to planet 4, for a total of 1 stop.