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 PYTHON3):

Solution:
import sys
import copy
input=sys.stdin.buffer.readline

t=int(input())
while t:
	t-=1
	n=int(input())
	ans=[]
	arr=list(map(int,input().split()))
	na=copy.deepcopy(arr)
	na.sort()
	arr1=list(map(int,input().split()))
	count0=0
	count1=0
	for x in arr1:
		if x==0:
			count1+=1
		else:
			count0+=1
	if count0>0 and count1>0:
		print("Yes")
	else:
		if na==arr:
			print("Yes")
		else:
			print("No")
"""
	if arr==na:
		print("Yes")
	else:
		i=0
		ans=[]
		while i<n:
			if na[i]==arr[i]:
				ans.append(arr1[i])
			else:
				for j in range(n):
					if arr[j]==na[i]:
						ans.append(arr1[j])
						break
			i+=1
		z=0
		for i in range(n):
			if na[i]==arr[i]:
				continue
			else:
				if ans[i]==arr1[i]:
					z=1
					break
		if z==1:
			print("No")
		else:
			print("Yes")
"""