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 PYTHON):

Solution:
import atexit, io, sys 
def find (a,k):
    for i in range(len(a)):
        if a[i]==k:
            return i
  
# A stream implementation using an in-memory bytes  
# buffer. It inherits BufferedIOBase. 

buffer = io.BytesIO() 

sys.stdout = buffer

  
# print via here 

@atexit.register 

def write(): 

    sys.__stdout__.write(buffer.getvalue()) 
for _ in range(input()):
    n=input()
    a=map(int,raw_input().split())
    b=map(int,raw_input().split())
    ok=1
    if (0 in b and 1 in b) or (sorted(a)==a):
        print"Yes"
    else:
        print"NO"
    continue

    for j in range(n,0,-1):
         k=max(a[:j])
         v=find(a,k)
         p=b[v]^1
         if v==j-1:
             pass
         elif b[j-1]==p:
             b[j-1],b[v]=b[v],b[j-1]
             a[j-1],a[v]=a[v],a[j-1]
         elif p in a[v+1:j]:
             t=find(a[v+1:j],p)
             b[v]=p
             b[v+1+t]=p^1
             a[v]=a[v+1+t]
             a[v+1+t]=a[j-1]
         else:
             print "NO";ok=0;break
    if ok:
        print"YES"