Problem: 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 ≠ 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 ≤ t ≤ 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 ≤ n ≤ 500) — the size of the arrays.

The second line contains n integers a_i (1 ≤ a_i ≤ 10^5) — the value of the i-th element.

The third line containts n integers b_i (b_i ∈ \{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 ≠ 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.

Solution (in PYTHON):

Solution:
def dfs(i, elements, example):
	if all([elements[jj][0] == example[jj] for jj in range(len(elements))]):
		return True
	a,b = 0,0
	for _,v in elements:
		if v:
			b +=1
		else:
			a +=1
	return  (a>0 and b>0)

	for j in range(i, len(elements)):
		aj,bj = elements[j]
		if aj == example[i] and (bj != elements[i][1] or i == j):
			elements[j], elements[i] =  elements[i], elements[j]
			if dfs(i + 1, elements, example):
				return True
			elements[j], elements[i] =  elements[i], elements[j]
	return False 
	

tt = int(raw_input())
for ti in range(tt):
	n = int(raw_input())
	ais = map(int, raw_input().split(' '))
	bis = map(int, raw_input().split(' '))
	#print zip(ais, bis),sorted(ais)

	print 'Yes' if dfs(0, zip(ais, bis), sorted(ais)) else 'No'