You are given two DNA sequences A and B. It is said that these two DNA sequences are related if there exists a non-decreasing sequence C of the same length, such that C_i = A_i or C_i = B_i. Find if the given sequences are related.

Input format:

The first line contains an integer, T, the number of test cases.

For each test case:

The first line contains an integer, N, the length of the DNA sequence.

The second line contains a sequence of space-separated integers describing species A.

The third line contains a sequence of space-separated integers describing species B.

Output Format

On a new line for each test case, print YES if a non-decreasing sequence of the same length can be found or NO if it cannot.

Constraints:

1 ≤ T ≤ 5

1 ≤ N ≤ 10⁵

0 ≤ A_i, B_i ≤ 10¹⁰

Sample:

Input
3
3
1 2 3
4 4 4
3
3 2 1
6 5 4
2
1 0
10 2
Input
YES
NO
YES