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:
# for t in range(int(input())):
#     n, x, m = [int(i) for i in input().split()]
#     l, r = x, x
#     # print(l, r)
#     for i in range(m):
#         cl, cr = [int(i) for i in input().split()]
#         # print(cl, r, l, cr)
#         if cl <= r and l <= cr:
#             l, r = min(l, cl), max(r, cr)
#         # print(l, r)
#     print(r - l + 1)


for t in range(int(input())):
    n = int(input())
    a = [int(i) for i in input().split()]
    b = [int(i) for i in input().split()]
    sorted = True
    i = 1
    while i < n and sorted:
        if a[i] >= a[i - 1]:
            i += 1
        else:
            sorted = False
    print('Yes' if 0 < sum(b) < n or sorted else 'No')




# 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