Problem Statement

You are given length-$N$ integer sequences $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_N)$, each consisting of $0$ and $1$. Let $A[i,j]$ denote the consecutive subsequence of $A$ from the $i$-th through the $j$-th element. If $i>j$, then $A[i,j]$ is a length-$0$ sequence. You can perform the following operation on $A$ any number of times:

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

Determine whether $A$ can be made to match $B$.

Solve $T$ test cases for each input file.

Constraints

• $1 \leq T \leq 10^5$
• $2 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq 1$
• $0 \leq B_i \leq 1$
• 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 answers in a total of $T$ lines. The $t$-th line should contain Yes if $A$ can be made to match $B$ for the $t$-th test case, and No otherwise.