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 JAVA):

Solution:
// var lineIdx = 0;
// var readline = () => {
//   var input = ["2", "4", "10 5 20 30", "0 1 0 1", "4", "10 5 20 30", "1 1 1 1"]
//   return input[lineIdx++];
// };
// var print = (str) => {
//   console.log(str);
// };

var n = readline().split(" ").map(function(x) { return parseInt(x); })[0];

var checksort = (arr) => {
  for(var i = 0; i < arr.length - 1; i++){
    if(arr[i] > arr[i+1]){
      return false;
    }
  }
  return true;
}

var step = () => {
  var size = readline().split(" ").map(function(x) { return parseInt(x); })[0];
  var numbers = readline().split(" ").map(function(x) { return parseInt(x); });
  var types = readline().split(" ").map(function(x) { return parseInt(x); });
  if(checksort(numbers)){
    print("Yes")
  }
  else {
    if(types.every(x => x == 1) || types.every(x => x == 0)){
      print("No")
    }
    else {
      print("Yes")
    }
  }
}

for(var i = 0; i < n; i++){
  step();
}