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:
#reattempt - after contest

import sys

def input():
	return sys.stdin.readline().rstrip()

t = int(input())
answers = []

def check_non_dec(array):
	for i in range(len(array) - 1):
		if array[i+1] < array[i]:
			return False
	return True


for _ in range(t):
	n = int(input())
	array = [int(i) for i in input().split()]
	bs = [int(i) for i in input().split()]

	arr1 = []
	arr2 = []
	for i in range(n):
		if bs[i] == 0:
			arr1.append(array[i])
		else:
			arr2.append(array[i])

	ans = True
	if (len(arr1) == 0 or len(arr2) == 0):
		ans = check_non_dec(arr1) and check_non_dec(arr2) 

	if ans:
		answers.append("Yes")
	else:
		answers.append("No")
		
print(*answers, sep = "\n")