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:
# Contest No.: 648
# Problem No.: B
# Solver:      JEMINI
# Date:        20200607

import sys
import heapq

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        aList = list(map(int, sys.stdin.readline().split()))
        bList = list(map(int, sys.stdin.readline().split()))
        list0 = []
        list1 = []
        for i in range(n):
            if bList[i]:
                list1.append(aList[i])
            else:
                list0.append(aList[i])
        
        if list0 and list1:
            print("Yes")
        else:
            flag = True
            if list0:
                for i in range(len(list0) - 1):
                    if list0[i] > list0[i + 1]:
                        flag = False
                        break
            if list1:
                for i in range(len(list1) - 1):
                    if list1[i] > list1[i + 1]:
                        flag = False
                        break
            if flag:
                print("Yes")
            else:
                print("No")
    return

if __name__ == "__main__":
    main()