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:
from sys import stdin, stdout
cin = stdin.readline
cout = stdout.write
mp = lambda: list(map(int, cin().split()))

def swap(x, i, j):
	t = x[i]
	x[i] = x[j]
	x[j] = t
	
t, = mp()
for _ in range(t):
	n, = mp()
	a = mp()
	b = mp()

	f = 0
	for i in range(n-1):
		if a[i] <= a[i+1]:
			continue
		else:
			x = y = 0
			for val in b:
				if val:
					x += 1
				else:
					y +=1
				if x and y:
					cout('yes\n')
					break
			else:
				cout('no\n')
			break
		'''
		mini = a[i]
		k = i
		for j in range(i+1, n):
			if a[i] > a[j]:
				if a[j] < mini:
					if b[i]!=b[j]:
						k = j
						mini = a[j]
					else:
						cout('noo\n')
						print(i, j, a[i], a[j], b[i], b[j])
						f = 1
						break
				#if a[j] <= mini:
				#f = 1
				#f b[i]!=b[j]:
		else:
			swap(a, i, k)
			swap(b, i, k)
		if f:
			break
		'''
	else:
		cout('yes\n')