Problem Statement

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

• Choose an integer i\ $(1 \leq i \leq N-2)$ such that A_i+A_{i+1}+A_{i+2} is even. Then, rearrange A_i, A_{i+1}, A_{i+2} as you like.

Determine whether it is possible to make A equal B.

Input

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

Output

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

Constraints

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

Sample Input 1

5
1 2 3 4 5
3 1 2 4 5

Sample Output 1

Yes

A_1+A_2+A_3 is 1+2+3=6, which is even, so you can choose i=1.
If you choose i=1 and rearrange A_1, A_2, A_3 into A_3, A_1, A_2, then A becomes (3, 1, 2, 4, 5).
Now A equals B, so you should print Yes.

Sample Input 2

5
1 2 4 6 5
5 1 4 2 6

Sample Output 2

No

Sample Input 3

9
2 10 4 3 6 2 6 8 5
2 4 10 3 8 6 6 2 5

Sample Output 3

Yes

见题面 Input 部分

见题面 Output 部分