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: $011\oplus 101 = 110)$.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分