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:
from math import *
from copy import *


t=int(input())
for ww in range(t):
    n=int(input())
    a=list(map(int,input().split()))
    c=deepcopy(a)
    c=sorted(c)
    b=list(map(int,input().split()))

    if b.count(0)==len(b) or b.count(1)==len(b):
        if a==c:
            print("Yes")
        else:
            print("No")
        continue
    l1=[]
    l2=[]
    for j in range(len(a)) :
        if b[j]==0:
            l1.append(a[j])
        else:
            l2.append(a[j])
    l1.sort()
    l2.sort()
    a=deepcopy(l1+l2)
    b=deepcopy(([0]*len(l1))+([1]*len(l2)))
    for i in range(n): 
        for j in range(0, n-i-1): 
            if a[j] > a[j+1] and b[j]!=b[j+1] : 
                a[j], a[j+1] = a[j+1], a[j] 
                b[j], b[j+1] = b[j+1], b[j] 
                # print("a= ",a)
                # print("b= ",b)
    # print(a)
    if a==c:
        print("Yes")
    else:
        print("No")