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:

# codeforces

# contest/1365/problem/B

def ALLSAME(brr, n):
    if brr.count(1) == n or brr.count(0) == n:
        return True
    return False

def is_SORT_possible(arr, brr, n):
    for i in range(n):
        for j in range(i+1, n):
            if arr[i] > arr[j]:
                if brr[i] != brr[j]:
                    arr[i],arr[j] = arr[j], arr[i]
                    brr[i],brr[j] = brr[j], brr[i]
    return arr == sorted(arr)

t = int(input())
for _ in range(t):
    n = int(input())
    arr = list(map(int, input().split()))
    brr = list(map(int, input().split()))
    
    #if is_SORT_possible(arr, brr, n):
    if arr == sorted(arr):
        print("Yes")
    else:
        if ALLSAME(brr, n):
            print("No")
        else:
            print("Yes")