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B. Trouble Sort

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAshish 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 $$$2$$$.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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