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:
import java.util.*;
import java.lang.*;
// StringBuilder uses java.lang
 
 
public class mC {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int test=0;test<t;test++) {
            int n = sc.nextInt();
            int cur = -1;
            int a = 0;
            boolean ok = true;
            boolean ok2 = false;
            for (int i=0;i<n;i++) {
                a=sc.nextInt();
                if (a<cur) {
                    ok=false;
                }
                cur=a;
            }
            int c = sc.nextInt();
            for (int i=1;i<n;i++) {
                a=sc.nextInt();
                if (a!=c) {
                    ok2=true;
                }
            }
            if (ok || ok2) {
                System.out.println("Yes");
            } else {
                System.out.println("No");
            }
        }
 
    }
    public static int findNthInArray(int[] arr,int val,int start,int o) {
        if (o==0) {
            return start-1;
        } else if (arr[start] == val) {
            return findNthInArray(arr,val,start+1,o-1);
        } else {
            return findNthInArray(arr,val,start+1,o);
        }
    }
    public static ArrayList<Integer> dfs(int at,ArrayList<Integer> went,ArrayList<ArrayList<Integer>> connect) {
        for (int i=0;i<connect.get(at).size();i++) {
            if (!(went.contains(connect.get(at).get(i)))) {
                went.add(connect.get(at).get(i));
                went=dfs(connect.get(at).get(i),went,connect);
            }
        }
        return went;
    } public static int[] bfs (int at, int[] went, ArrayList<ArrayList<Integer>> queue, int numNodes, ArrayList<ArrayList<Integer>> connect) {
        if (went[at]==0) {
            went[at]=queue.get(numNodes).get(1);
            for (int i=0;i<connect.get(at).size();i++) {
                if (went[connect.get(at).get(i)]==0) {
                    ArrayList<Integer> temp = new ArrayList<>();
                    temp.add(connect.get(at).get(i));
                    temp.add(queue.get(numNodes).get(1)+1);
                    queue.add(temp);
                }
            }
            
        }
        if (queue.size()==numNodes+1) {
            return went;
        } else {
            return bfs(queue.get(numNodes+1).get(0),went, queue, numNodes+1, connect);
        }
    }
    public static long fastPow(int base,long exp,long mod) {
        if (exp==0) {
            return 1;
        } else {
            if (exp % 2 == 1) {
                long z = fastPow(base,(exp-1)/2,mod);
                return ((((z*base) % mod) * z) % mod);
            } else {
                long z = fastPow(base,exp/2,mod);
                return ((z*z) % mod);
            }
        }
    }
    public static long fastPow(int base,long exp) {
        if (exp==0) {
            return 1;
        } else {
            if (exp % 2 == 1) {
                long z = fastPow(base,(exp-1)/2);
                return ((((z*base)) * z));
            } else {
                long z = fastPow(base,exp/2);
                return ((z*z));
            }
        }
    }
    public static int firstLarger(int val,ArrayList<Integer> ok,int left,int right) {
        if (ok.get(right)<=val) {
            return -1;
        }
        if (left==right) {
            return left;
        } else if (left+1==right) {
            if (val<ok.get(left)) {
                return left;
            } else {
                return right;
            }
        } else {
            int mid = (left+right)/2;
            if (ok.get(mid)>val) {
                return firstLarger(val,ok,left,mid);
            } else {
                return firstLarger(val,ok,mid+1,right);
            }
        }
    }
}