A13516. Trouble Sort

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).

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 $2$ .