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:
def read_int():
	return int(input())

def read_lst():
	return list(map(int, input().split()))

def dec(x):
	return x - 1

def inc(x):
	return x + 1
	
def odd(x):
	return x % 2 != 0

def update_type(x,b):
	t_0,t_1 = b
	if(x == 0):
		return (inc(t_0),t_1)
	else:
		return (t_0,inc(t_1))
		
def is_sorted(lst):

	def update_flag(lst,idx):
		return lst[dec(idx)] >= lst[dec(dec(idx))]
	
	def is_sorted_helper(lst,idx,flag):
		if(idx == 1):
			return flag
		else:
			return is_sorted_helper(lst,dec(idx),(flag and (update_flag(lst,idx))))
	
	return is_sorted_helper(lst,len(lst),True)

def is_sortable(lst_item,lst):

	def are_both_types_count_equal(lst,idx,type_01):
		type_0, type_1 = type_01
		if(idx == 0):
			if(type_0 != 0 and type_1 != 0):
				return (abs(type_0 - type_1) >= 1 or (type_0 == type_1))
			else:
				return False
		else:
			return are_both_types_count_equal(lst,dec(idx),update_type(lst[idx-1],(type_0,type_1)))

	if(is_sorted(lst_item) or are_both_types_count_equal(lst, len(lst), (0,0))):
		return "Yes"
	else:
		return "No"

def trouble_sort_handler(test_cases):
	if(test_cases != 0):
		size = read_int()
		lst = read_lst()
		type_info_lst = read_lst()
		print(is_sortable(lst,type_info_lst))
		return trouble_sort_handler(dec(test_cases))

def main():
	test_cases = read_int()
	trouble_sort_handler(test_cases)

main()