Problem Statement

You are given two sequences, each of length $N$, consisting of non-negative integers: $A=(A_1,A_2,\ldots,A_{N})$ and $B=(B_1,B_2,\ldots,B_{N})$.

Determine whether it is possible to make $A$ equal to $B$ by performing the operation below at most $70000$ times. If it is possible, present a specific sequence of operations that achieves it.

• Choose an integer $K\ (1\le K \le N)$. For every integer $i\ (2\leq i \leq K)$, simultaneously replace the value of $A_i$ with $A_{i-1} \oplus A_i$.

Here, $\oplus$ denotes bitwise $\mathrm{XOR}$.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A\oplus B$, is defined as follows: When $A\oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ are $1$, and $0$ otherwise. For example, $3\oplus 5 = 6$ (in base two: $011\oplus 101 = 110$).

Constraints

• $2 \leq N \leq 1000$
• $0 \leq A_i, B_i < 2^{60}$
• All values in input are integers.

Input

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

If it is impossible to make $A$ equal to $B$ in at most $70000$ operations, print No. If it is possible, print a sequence of operations that achieves it in the following format, where $M$ is the number of operations, and $K_i$ is the integer chosen in the $i$-th operation:

Yes
M
K_1 K_2 \ldots K_M

If multiple solutions exist, any of them will be accepted.