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:
def merge(arr, l, m, r): 
    n1 = m - l + 1
    n2 = r- m 
  
    # create temp arrays 
    L = [0] * (n1) 
    R = [0] * (n2) 
  
    # Copy data to temp arrays L[] and R[] 
    for i in range(0 , n1): 
        L[i] = arr[l + i] 
  
    for j in range(0 , n2): 
        R[j] = arr[m + 1 + j] 
  
    # Merge the temp arrays back into arr[l..r] 
    i = 0     # Initial index of first subarray 
    j = 0     # Initial index of second subarray 
    k = l     # Initial index of merged subarray 
  
    while i < n1 and j < n2 : 
        if L[i] <= R[j]: 
            arr[k] = L[i] 
            i += 1
        else: 
            arr[k] = R[j] 
            j += 1
        k += 1
  
    # Copy the remaining elements of L[], if there 
    # are any 
    while i < n1: 
        arr[k] = L[i] 
        i += 1
        k += 1
  
    # Copy the remaining elements of R[], if there 
    # are any 
    while j < n2: 
        arr[k] = R[j] 
        j += 1
        k += 1
  
# l is for left index and r is right index of the 
# sub-array of arr to be sorted 
def mergeSort(arr,l,r): 
    if l < r: 
  
        # Same as (l+r)//2, but avoids overflow for 
        # large l and h 
        m = (l+(r-1))//2
  
        # Sort first and second halves 
        mergeSort(arr, l, m) 
        mergeSort(arr, m+1, r) 
        merge(arr, l, m, r) 
t=int(input())
for i in range(t):
    n=int(input())
    a=list(map(int,input().split()))
    b=list(map(int,input().split()))
    num1=[]
    for j in range(n):
        num1.append(a[j])
    mergeSort(num1,0,n-1)
    lis=[]
    arr1=0
    arr2=0
    for j in range(n):
        if a[j]!=num1[j]:
            lis.append(j)
        if b[j]==1:
            arr1+=1
        if b[j]==0:
            arr2+=1
    l=len(lis)
    if l==0:
        print("Yes")
    else:
        if arr1==0 or arr2==0:
            print("No")
        else:
            print("Yes")