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Time Limit: 1000 ms

Memory Limit: 65535 ms

Description

There are n numbers( 1 ~ n ) stand in an order . Now give you a sequence.Please deal with the n numbers using the sequence.
such as :
n numbers : 1 2 3 4 5  ( sequence 1 )
a sequence: 2 1 4 3 5  ( sequence 2 )


sequence 1 change into 2 1 4 3 5 by the sequence 2 once.
sequence 1 change into 1 2 3 4 5 by the sequence 2 twice.

so the answer is 2.It means sequence 1 need two times go back to itself.

Input

There are multiple test cases.The first line contain a integer t( t <= 1000 ), indicate t cases.For each case,the first line contain a integer n.next two line contain two sequence (sequence 1 and sequence 2 )

Output

For each case ,please print the answer mod 100007.

Sample Input

1
5
2 1 3 4 5
1 3 2 4 5

HINT:
样例解释:第一步: 2 3 1 4 5      第二步: 2 1 3 4 5 

Sample Output

2

Hint

None

Source

水果杯之窦煜峰专场练习赛

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