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
import math
from collections import defaultdict,deque
import heapq
t=int(sys.stdin.readline())
for _ in range(t):
	n=int(sys.stdin.readline())
	a=list(map(int,sys.stdin.readline().split()))
	b=list(map(int,sys.stdin.readline().split()))
	z=True
	for i in range(n):
		'''numi=a[i]
		sti=b[i]
		indi=i
		indj,stj=i,b[i]
		cnt0,cnt1=0,0
		ind0=-1
		ind1=-1
		for j in range(i,n):
			if a[j]<numi:
				numi=a[j]
				indj=j
				stj=b[j]
			if b[j]==0:
				ind0=j
			else:
				ind1=j
			cnt0+=(b[j]==0)
			cnt1+=(b[j]==1)
		print(indj,'indj',cnt0,'cnt0',cnt1,'cnt')
		print(a,'a')
		print(b,'b')
		if indj!=i:
			if stj!=sti:
				a[i],a[indj]=a[indj],a[i]
				b[i],b[indj]=b[indj],b[i]
			else:
				if stj==1:
					if cnt0==0:
						z=False
						print('No')
						break
					else:
						a[i],a[ind0]=a[ind0],a[i]
						b[i],b[ind0]=b[ind0],b[i]
						a[i],a[indj]=a[indj],a[i]
						b[i],b[indj]=b[indj],b[i]
				else:
					if cnt1==0:
						z=False
						print('No')
						break
					else:
						a[i],a[ind1]=a[ind1],a[i]
						b[i],b[ind1]=b[ind1],b[i]
						a[i],a[indj]=a[indj],a[i]
						b[i],b[indj]=b[indj],b[i]

	if z:
		print('Yes')'''
	z=True
	cnt0,cnt1=0,0
	for i in range(n):
		if i+1<n:
			if a[i+1]<a[i]:
				z=False
		cnt0+=(b[i]==0)
		cnt1+=(b[i]==1)
	if z:
		print('Yes')
	else:
		if cnt0 !=0 and cnt1!=0:
			print('Yes')
		else:
			print('No')