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
# from collections import Counter
# from math import ceil,log

# def gcd(a, b):
# 	if(a==0):
# 		return b 
# 	return gcd(b%a,a)

# def sieve(n): 
# 	prime=[True for i in range(n+1)]
# 	p=2
# 	while(p*p<=n): 
# 		if (prime[p]==True): 
# 			for i in range(p*p,n+1,p): 
# 				prime[i]=False
# 		p+=1
# 	prime[0]=False
# 	prime[1]=False
# 	return prime 

# alpha=['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']
# mod=10**9+7

fast_reader=sys.stdin.readline

def input():
	return fast_reader().strip()

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

def sep_input():
	return map(int, input().split())

#_______________________________________________________________________________________________________________________________________


def bubbleSort(arr,b): 
	n = len(arr) 
	# Traverse through all array elements 
	for i in range(n): 
		# Last i elements are already in place 
		for j in range(0, n-i-1): 
			# traverse the array from 0 to n-i-1 
			# Swap if the element found is greater 
			# than the next element 
			if arr[j] > arr[j+1] and b[j]!=b[j+1] : 
				arr[j], arr[j+1] = arr[j+1], arr[j]
				b[j] , b[j+1] = b[j+1] , b[j]
	return arr 
	
for _ in range(int(input())):
	n=int(input())
	a=list_input()
	b=list_input()
	if(a==sorted(a)):
		print('YES')
		continue
	if(len(set(b))==1):
		print('NO')
		continue
	z=[]
	o=[]
	for i in range(n):
		if(b[i]==0):
			z.append(a[i])
		else:
			o.append(a[i])
	z.sort()
	o.sort()
	x=0
	y=0
	for i in range(n):
		if(b[i]==0):
			a[i]=z[x]
			x+=1
		else:
			a[i]=o[y]
			y+=1
	l=bubbleSort(a,b)
	if(l==sorted(l)):
		print('YES')
	else:
		print('NO')