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:
# May the Speedforce be with us...
'''
problem statement achhe se padhna hai
age se bhi dekhna hai, piche se bhi dekhna hai
'''
#from math import gcd,ceil,sin,radians,cos
from math import ceil
#from bisect import insort
#from collections import defaultdict as dd
def lcm(a,b):
	return (a*b)//gcd(a,b)
def inin():
	return int(input())
def inar():
	return list(map(int,input().split()))
def ar(element,size):
	return [element for i in range(size)]
def yes():
	print('Yes')
def no():
	print('No')
'''
def countDivisibles(A, B, M): #count numbers in the range[A,B] which are divisible by M
    if (A % M == 0): 
        return ((B // M) - (A // M)) + 1
    return ((B // M) - (A // M)) 
	
def  countSetBits(n): #count the number of set bits in the binary representation of an integer
    count = 0
    while (n): 
        count += n & 1
        n >>= 1
    return count
def digitsum(num): #return the sum of dogots of a number
	su=0
	while(num):
		su+=num%10
		num//=10
	return su
'''


Testcase=inin()
for _ in range(Testcase):
	n=inar()
	a=inar()
	b=inar()
	if a==sorted(a):
		yes()
	elif b.count(1)>0 and b.count(0)>0:
		yes()
	else:
		no()