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.io.*;
import java.util.*;

public class CF1365B {

    static class Element implements  Comparable<Element>{
        int position;
        int cost;
        int type;
        boolean done;
        Element(int position,int cost,int type,boolean done){
            this.position = position;
            this.cost = cost;
            this.type = type;
            this.done = done;
        }
        public  int compareTo(Element other){
            if(this.cost == other.cost)
                return 0;
            else if(this.cost > other.cost)
                return 1;
            else
                return -1;
        }
    }
    public static void main(String[] args) throws IOException{
        Reader input = new Reader();
        PrintWriter pw = new PrintWriter(System.out);
        // code goes here

        int t = input.nextInt();
        while (t > 0){
            int n = input.nextInt();
            int[] cost = new int[n+1];
            int[] type = new int[n+1];
            for(int i = 1; i <= n;i++){
                cost[i] = input.nextInt();
            }
            for(int i = 1;i <= n;i++){
                type[i] = input.nextInt();
            }
            Element[] arr = new Element[n];
            int pos = 0;

            for(int i = 1;i <= n;i++){
                arr[pos] = new Element(i,cost[i],type[i],false);
                pos++;
            }
            Arrays.sort(arr);

//            for(Element e : arr){
//                pw.println(e.position + " " + e.cost + " " + e.type + " " + e.done);
//            }

            boolean con = true;
            for(int i = 0;i < n;i++){
                if(arr[i].position == i+1){

                }
                else{
                    boolean con2 = false;

                    int index = -1;
                    for(int j = 0;j < n;j++){
                        if(j != i  &&  arr[j].position == i+1){
                            index = j;
                            if(arr[j].type != arr[i].type){
                                con2 = true;
                            }
                            break;
                        }
                    }
                    if(index == -1){
                        con = false;
                       // pw.println("Here");
                       // pw.println(arr[i].position + " " + arr[i].cost + " " + arr[i].type + " " + arr[i].done);
                        break;
                    }
                    if(con2){
                        int temp_pos = arr[i].position;
                        arr[i].position = arr[index].position;
                        arr[index].position = temp_pos;

                    }
                    else{
                        int index2 = -1;
                        for(int j = 0;j < n;j++){
                           if(j != index  && arr[j].type != arr[index].type){
                               index2 = j;
                               break;
                           }
                        }
                        if(index2 == -1){
                            con = false;
                           // pw.println("Here2");
                            break;
                        }
                        else{
                           // pw.println("moved " + arr[index].position + " " + arr[index2].position);
                            int temp_pos = arr[index].position;
                            arr[index].position = arr[index2].position;
                            arr[index2].position = temp_pos;


                            temp_pos = arr[i].position;
                            arr[i].position = arr[index2].position;
                            arr[index2].position = temp_pos;
                           // pw.println("Swapped" + arr[i].position + " " + arr[index2].position);

                        }
                    }
                }
            }

            if(con){
                pw.println("Yes");
            }
            else{
                pw.println("No");
            }

            t--;
        }

        pw.flush();
        pw.close();
    }
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
}