B. Trouble Sort
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

    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).

    Example
    Input
    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
    
    Output
    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 $$$2$$$.