Problem Statement

You are given two sequences of N numbers: $A=(A_1,A_2,\ldots,A_N)$ and $B=(B_1,B_2,\ldots,B_N)$.
Takahashi can repeat the following operation any number of times (possibly zero).

Choose three pairwise distinct integers i, j, and k between 1 and N.
Swap the i-th and j-th elements of A, and swap the i-th and k-th elements of B.

If there is a way for Takahashi to repeat the operation to make A and B equal, print Yes; otherwise, print No.
Here, A and B are said to be equal when, for every $1\leq i\leq N$, the i-th element of A and that of B are equal.

Input

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

Output

Print Yes if there is a way for Takahashi to repeat the operation to make A and B equal, and print No otherwise.

Constraints

• $3 \leq N \leq 2\times 10^5$
• $1\leq A_i,B_i\leq N$
• All values in the input are integers.

Sample Input 1

3
1 2 1
1 1 2

Sample Output 1

Yes

Performing the operation once with (i,j,k)=(1,2,3) swaps A_1 and A_2, and swaps B_1 and B_3,
making both A and B equal to (2,1,1). Thus, you should print Yes.

Sample Input 2

3
1 2 2
1 1 2

Sample Output 2

No

There is no way to perform the operation to make A and B equal, so you should print No.

Sample Input 3

5
1 2 3 2 1
3 2 2 1 1

Sample Output 3

Yes

Sample Input 4

8
1 2 3 4 5 6 7 8
7 8 5 6 4 3 1 2

Sample Output 4

No

见题面 Input 部分

见题面 Output 部分