For an array A of N integers, define

• An array P of length N, where P_{i} is the number of distinct elements in the subarray A[1:i] of A.
• An array S of length N, where S_{i} is the number of distinct elements in the subarray A[i:N] of A.

You are given arrays P and S. Determine whether there exists an array A corresponding to the given P and S arrays.

------ Input Format ------

• The first line of input contains a single integer T, denoting the number of test cases. The description of the test cases follows.
• Each test case consists of three lines of input.
• The first line of each test case contains a single integer N.
• The second line of each test case contains $N space-separated integers P_{1}, P_{2} \ldots P_{N}$.
• The third line of each test case contains $N space-separated integers S_{1}, S_{2} \ldots S_{N}$.

------ Output Format ------

For each test case, output the answer on a new line: if there does not exist any array A producing such P and S arrays, then output NO, otherwise output YES

You can output each letter in any case.

------ Constraints ------

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{5}$
$1 ≤ P_{i} ≤ N$
$1 ≤ S_{i} ≤ N$
- The sum of $N$ over all test cases doesn't exceed $2\cdot 10^{5}$

----- Sample Input 1 ------
4
3
1 2 3
3 2 1
4
2 2 3 3
3 2 2 1
2
1 1
1 1
3
1 2 1
2 2 1

----- Sample Output 1 ------
YES
NO
YES
NO

----- explanation 1 ------
Test case $1$: We have $P = [1, 2, 3]$ and $S = [3, 2, 1]$.

Consider $A = [1, 2, 3]$.
- The number of distinct elements in the $1$st prefix $[1]$ is $1$.
- The number of distinct elements in the $2$nd prefix $[1,2]$ is $2$.
- The number of distinct elements in the $3$rd prefix $[1,2,3]$ is $3$.

and
- The number of distinct elements in the $1$st suffix $[1,2,3]$ is $3$.
- The number of distinct elements in the $2$nd suffix $[2,3]$ is $2$.
- The number of distinct elements in the $3$rd suffix $[3]$ is $1$.

Clearly $A$ produces the given $P$ and $S$.

Test case $2$: We have $P =[2,2,3,3]$ , $S =[3,2,2,1]$.

It can be proven that there does not exist any array $A$ which produces the given $P$ and $S$.

Test case $3$: We have $P =[1,1]$, $S =[1,1]$.

Consider $A = [7,7]$.
- The number of distinct elements in the $1$st prefix $[7]$ is $1$.
- The number of distinct elements in the $2$nd prefix $[7,7]$ is $1$.

and
- The number of distinct elements in the $1$st suffix $[7,7]$ is $1$.
- The number of distinct elements in the $2$nd suffix $[7]$ is $1$.

Clearly $A$ produces the given $P$ and $S$.

Test case $4$: $P = [1,2,1]$ , $S =[2,2,1]$.

It can be proven that there does not exist any array $A$ which produces the given $P$ and $S$.

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