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 $B$.

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.

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.