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:
import sys
from typing import List
input = sys.stdin.readline
import math

############ ---- Input Functions ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input().strip()
    return(list(s[:len(s)]))
def invr():
    return(map(int,input().strip().split()))



def from_file(f):
    return f.readline


def solution(A: List[int], B: List[int]):
   a0, a1 = -float('inf'), -float('inf')
   c0, c1 = 0, 0
   for ai, bi in zip(A, B):
       if bi == 0:
           c0 += 1
           if ai >= a0:
               a0 = ai
           else:
               a0 = float('inf')
       else:
           c1 += 1
           if ai >= a1:
               a1 = ai
           else:
               a1 = float('inf')
   if a0 < float('inf') and a1 < float('inf'):
       return 'Yes'
   if a0 == float('inf') and a1 == float('inf'):
       if c0 > 0 and c1 > 0:
           return 'Yes'
       return 'No'

   if a1 == float('inf'):
       a0, a1 = a1, a0
       c0, c1 = c1, c0

   if c1 > 0:
       return 'Yes'
   return 'No'





# with open('2.txt') as f:
#     input = from_file(f)
t = inp()
for _ in range(t):
    n = inp()
    A = inlt()
    B = inlt()
    print(solution(A, B))