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:
t=int(input())
for _ in range(t):
    n=int(input())
    A=list(map(int,input().split(" ")))
    B=list(map(int,input().split(" ")))
    C=sorted(A)
    #print(C,A)
    if C==A:
        print("YES")
    elif 1 in B and 0 in B:
        print("YES")
    else:
        print("NO")    

    # # for i in range(n):
    # #     for j in range(i+1,n):
    # #         mini=A[i]
    # #         ind=i
    # #         if A[i]>A[j] and B[i]!=B[j]:
    # #             if A[j]<mini:
    # #                 mini=A[j]
    # #                 ind=j
                
    # #     A[i],A[ind]=A[ind],A[i]
    # #     B[i],B[ind]=B[ind],B[i]
    # for i in range(n):
    #     for j in range(i+1,n):
    #         if A[i]>A[j] and B[i]!=B[j]:
    #             A[i],A[j]=A[j],A[i]
    #             B[i],B[j]=B[j],B[i]
    #     print(A)
    #     print(B)          
    # f=1   
       
    # for i in range(n):
    #     if A[i]<=A[i+1]:
    #         continue
    #     else:
    #         print("NO")
    #         f=0
    #         break
    # if f==1:
    #     print("YES")