Problem Statement

You are given sequences of positive integers of length $N$: $A=(A_1,A_2,\ldots,A_N),B=(B_1,B_2,\ldots,B_N)$.

Determine whether there exists an integer sequence $X=(X_1,X_2,\ldots,X_N)$ that satisfies all the following conditions, and if it exists, find one.

• $-10^8\le X_i\le 10^8$ $(1\le i\le N)$
• $\displaystyle \sum_{i=1}^N A_iX_i > 0$
• $\displaystyle \sum_{i=1}^N B_iX_i < 0$

You are given $T$ test cases, so find the answer for each.

Constraints

• $1\le T\le 2\times 10^5$
• $1\le N\le 2\times 10^5$
• $1\le A_i,B_i\le 10^5$
• 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
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_N

Output

Output your solutions for the test cases in order, separated by newlines.

For each test case, if there is no $X$ that satisfies all conditions, output No.

Otherwise, output an $X$ that satisfies all conditions in the following format:

Yes
X_1 X_2 \ldots X_N

If there are multiple $X$ that satisfy the conditions, you may output any of them.