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.

Sample Input 1

3
1 2 0
1 2 3

Sample Output 1

Yes
2
2 3

In this output, the sequence $A$ is changed as follows:

• Initially: $A=(1, 2, 0)$.
• After the $1$-st operation: $A=(1, 3, 0)$.
• After the $2$-nd operation: $A=(1, 2, 3)$.

After the two operations, $A$ and $B$ are equal, achieving the objective.

Sample Input 2

2
10 100
1 0

Sample Output 2

No

Sample Input 3

2
1152921504606846975 0
1152921504606846975 0

Sample Output 3

Yes
0