Problem Statement

You are given integer sequences $A=(A_1,A_2,\dots,A_N),\; B=(B_1,B_2,\dots,B_N)$ of length $N$ consisting of $0$ and $1$. Let $A[i,j]$ denote the contiguous subsequence from the $i$-th through $j$-th elements of sequence $A$. If $i>j$, $A[i,j]$ is a sequence of length $0$. You can perform the following operation on $A$ at most $\lfloor\frac{N}{2}\rfloor$ times:

• Choose four integers $a,b,c,d$ that satisfy the following three conditions:
• $1 \leq a \leq b < c \leq d \leq N$
  • $b-a=d-c$
  • $\sum_{i=a}^{b}{A_i}=\sum_{i=c}^{d}{A_i}$
• Swap $A[a,b]$ and $A[c,d]$. More precisely, replace $A$ with the concatenation of $A[1,a-1]$, $A[c,d]$, $A[b+1,c-1]$, $A[a,b]$, $A[d+1,N]$ in this order.

Determine whether it is possible to make $A$ match $B$, and if possible, construct one sequence of operations.

Solve $T$ test cases per input.

Constraints

• $1 \leq T \leq 25000$
• $2 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq 1$
• $0 \leq B_i \leq 1$
• The sum of $N$ over all test cases is at most $2\times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
case_1
case_2
\vdots
case_T

Each case is given in the following format:

N
A_1 A_2 \dots A_N
B_1 B_2 \dots B_N

Output

Output the answer in the following format:

output_1
output_2
\vdots
output_T

Here, $output_t$ represents the output for the $t$-th test case. For each case, if you can make $A$ match $B$, let $K$ be the number of operations required and $(a_k,b_k,c_k,d_k)$ be the values chosen in the $k$-th operation, then output in the following format:

Yes
K
a_1 b_1 c_1 d_1
a_2 b_2 c_2 d_2
\vdots
a_K b_K c_K d_K

If it is impossible to make $A$ match $B$, output No.