Problem Statement

You are given integer sequences of length N each: $A=(A_1,A_2,\cdots,A_N)$ and $B=(B_1,B_2,\cdots,B_N)$.
You can repeat the following operation any number of times.

• Choose an integer $i (1 \leq i \leq N-2)$ and let x,y,z be the current values of A_i,A_{i+1},A_{i+2}, respectively.
  Then, replace the values of A_i,A_{i+1},A_{i+2} with z,x,y, respectively.

Determine whether it is possible to make A equal B.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$
$B_1 B_2 \cdots B_N$

Output

If it is possible to make A equal B, print Yes; otherwise, print No.

Constraints

• $3 \leq N \leq 5000$
• $1 \leq A_i,B_i \leq 5000$
• All values in input are integers.

Sample Input 1

4
3 1 4 5
4 1 5 3

Sample Output 1

Yes

We should do the following.

• Initially, we have A=(3,1,4,5).
• Do the operation with i=1, making A=(4,3,1,5).
• Do the operation with i=2, making A=(4,5,3,1).
• Do the operation with i=2, making A=(4,1,5,3).

Sample Input 2

3
1 2 2
2 1 2

Sample Output 2

Yes

Sample Input 3

3
1 2 3
2 3 4

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分