P13822 「Diligent-OI R2 B」Dew and Frost Gleam

Ns6 couldn't solve [ARC146E](/problem/AT_arc146_e), so he created this problem.

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.**

**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 $b_1,b_2,\dots,b_n$.

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.**

#### 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.