Description

A sequence $a_1,a_2,\dots,a_n$ is called a polyline if and only if for $i=1,2,\dots,n-1$, the condition $|a_i-a_{i+1}|=1$ is satisfied. Specifically, a sequence of length $1$ is also considered a polyline.

Given $n$ and two sequences $a$ and $b$ of length $n$, where both $a$ and $b$ are polylines, you can perform the following operation on $a$ any number of times:

Choose an integer $1\le i\le n$ and modify $a_i$ to any value, but you must ensure that after the modification, the sequence $a$ remains a polyline.

The question is: Can you make $a$ equal to $b$? Note: You do not need to print the operation steps.

Input Format

Note that this problem requires efficient input and output methods.

The input consists of multiple test cases. The first line contains $T$, the number of test cases.

For each test case:

The first line contains $n$.

The second line contains $n$ integers $a_1,a_2,\dots,a_n$.

The third line contains $n$ integers $b_1,b_2,\dots,b_n$.

Output Format

For each test case, output one line. If it is impossible to make $a$ equal to $b$, output No; otherwise, output Yes. Note: You do not need to print the operation steps.

3
1
1
2
4
1 2 3 4
3 2 3 2
2
1 2
2 1

Yes
Yes
No

Hint

Sample #1 Explanation

First test case: $\{1\}\rarr\{2\}$.

Second test case: $\{1,2,3,4\}\rarr\{3,2,3,4\}\rarr\{3,2,3,2\}$.

Third test case: It can be proven that there is no solution.

Data Range

Let $N$ be the sum of $n$ across all test cases in a single test point.

For $100\%$ of the data, $1\le T\le10^6,1\le n\le10^6,1\le N\le10^6,1\le a_i\le10^9$.

• Testcase 1: $n=1$.
• Testcase 2: $n\le2$.
• Testcase 3: $T\le 5,n\le 4,a_i,b_i\le4$.
• Testcase 4: For any $1\le i\le n$, $b_i=a_i+1$.
• Testcase 5: No additional constraints.