Trouble Sort
Description
Ashish has $n$ elements arranged in a line.
These elements are represented by two integers $a_i$ — the value of the element and $b_i$ — the type of the element (there are only two possible types: $0$ and $1$). He wants to sort the elements in non-decreasing values of $a_i$.
He can perform the following operation any number of times:
- Select any two elements $i$ and $j$ such that $b_i \ne b_j$ and swap them. That is, he can only swap two elements of different types in one move.
Tell him if he can sort the elements in non-decreasing values of $a_i$ after performing any number of operations.
The first line contains one integer $t$ $(1 \le t \le 100)$ — the number of test cases. The description of the test cases follows.
The first line of each test case contains one integer $n$ $(1 \le n \le 500)$ — the size of the arrays.
The second line contains $n$ integers $a_i$ $(1 \le a_i \le 10^5)$ — the value of the $i$-th element.
The third line containts $n$ integers $b_i$ $(b_i \in \{0, 1\})$ — the type of the $i$-th element.
For each test case, print "Yes" or "No" (without quotes) depending on whether it is possible to sort elements in non-decreasing order of their value.
You may print each letter in any case (upper or lower).
Input
The first line contains one integer $t$ $(1 \le t \le 100)$ — the number of test cases. The description of the test cases follows.
The first line of each test case contains one integer $n$ $(1 \le n \le 500)$ — the size of the arrays.
The second line contains $n$ integers $a_i$ $(1 \le a_i \le 10^5)$ — the value of the $i$-th element.
The third line containts $n$ integers $b_i$ $(b_i \in \{0, 1\})$ — the type of the $i$-th element.
Output
For each test case, print "Yes" or "No" (without quotes) depending on whether it is possible to sort elements in non-decreasing order of their value.
You may print each letter in any case (upper or lower).
Samples
5
4
10 20 20 30
0 1 0 1
3
3 1 2
0 1 1
4
2 2 4 8
1 1 1 1
3
5 15 4
0 0 0
4
20 10 100 50
1 0 0 1
Yes
Yes
Yes
No
Yes
Note
For the first case: The elements are already in sorted order.
For the second case: Ashish may first swap elements at positions $1$ and $2$, then swap elements at positions $2$ and $3$.
For the third case: The elements are already in sorted order.
For the fourth case: No swap operations may be performed as there is no pair of elements $i$ and $j$ such that $b_i \ne b_j$. The elements cannot be sorted.
For the fifth case: Ashish may swap elements at positions $3$ and $4$, then elements at positions $1$ and $2$.