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 javafx.util.Pair;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;


public class q_2 {
    static Scanner sc;
    static FastReader fr;
    public static void main(String[] args){
        sc = new Scanner(System.in);
        fr = new FastReader();
        int test = sc.nextInt();
        for(int t=0; t<test; t++){
            int n = sc.nextInt();
            int[] vals = new int[n];
            for(int i=0; i<n; i++){
                vals[i] = sc.nextInt();
            }
            boolean dualType = false;
            int type = sc.nextInt();
            for(int i=1; i<n; i++){
                int x = sc.nextInt();
                if(x != type ){
                    dualType = true;
                }
            }
            if(dualType){
                System.out.println("Yes");
            }
            else {
                // if vals is already sorted
                boolean isSorted = isSorted(vals, n);
                if(isSorted){
                    System.out.println("Yes");
                }
                else {
                    System.out.println("No");
                }
            }
        }
    }

    private static boolean isSorted(int[] vals, int n) {
        //System.out.println(n+" is n and size is "+vals.length);
        int base = vals[0];
        boolean res = true;
        for(int i=1; i<n; i++){
            if(vals[i]<vals[i-1]){
                res = false;
            }
        }
        return res;
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static Integer[] getIntArrayFromSingleLine(){
        List<Integer> list = new LinkedList<>();
        String[] str = fr.nextLine().split(" ");
        for(String s: str){
            list.add(Integer.parseInt(s));
        }
        Integer[] arr = new Integer[list.size()];
        return list.toArray(arr);
    }

    public static Long[] getLongArrayFromSingleLine(){
        List<Long> list = new LinkedList<>();
        String[] str = fr.nextLine().split(" ");
        for(String s: str){
            list.add(Long.parseLong(s));
        }
        Long[] longs = new Long[list.size()];
        return list.toArray(longs);
    }

    public static Double[] getDoubleArrayFromSingleLine(){
        List<Double> list = new LinkedList<>();
        String[] str= fr.nextLine().split(" ");
        for(String s: str){
            list.add(Double.parseDouble(s));
        }
        Double[] doubles = new Double[list.size()];
        return list.toArray(doubles);
    }

    public static int[] getArray(int n){
        int[] arr = new int[n];
        for(int i=0; i<n; i++){
            arr[i] = fr.nextInt();
        }
        return arr;
    }

    public static long[] getLongArray(int n){
        long[] res = new long[n];
        for(int i=0; i<n; i++){
            res[i] = fr.nextLong();
        }
        return res;
    }

    public static double[] getDoubleArray(int n){
        double[] arr = new double[n];
        for(int i=0; i<n ; i++){
            arr[i] = fr.nextDouble();
        }
        return arr;
    }

    public static char[] getCharArray(){
        return fr.next().toCharArray();
    }

    public static String[] getStringArray(int n){
        String[] strings = new String[n];
        for(int i=0; i<n; i++){
            strings[i] = fr.next();
        }
        return strings;
    }

    // Get GCD
    public static int getGCD(int a, int b){
        return (a==0 ? b : getGCD(b%a, a));
    }

    public static int getGCD(int[] arr){
        int n = arr.length;
        if(n==0){
            return -1;
        }
        int res = arr[0];
        for(int i=1; i<n; i++){
            res = getGCD(res, arr[i]);
        }
        return res;
    }

    // Get all prime numbers till N using seive of Eratosthenes
    public static List<Integer> getPrimesTill(int n){
        boolean[] arr = new boolean[n+1];
        List<Integer> primes = new LinkedList<>();
        for(int i=2; i<=n; i++){
            if(!arr[i]){
                primes.add(i);
                for(int j=(i*i); j<=n; j+=i){
                    arr[j] = true;
                }
            }
        }
        return primes;
    }


    // This method returns list of PrimeFactors of a number in O(sqrt(N));
    public static Map<Integer,Integer> getPrimeFactors(long n){
        Map<Integer,Integer> res = new HashMap<>();
        int sqrt = (int) Math.sqrt(n);
        if(n%2 == 0){
            int c = 0;
            while(n%2==0){
                c++;
                n/=2;
            }
            res.put(2,c);
        }
        for(int i=3; i<=sqrt; i+=2){
            if(n%i == 0) {
                int c = 0;
                while (n % i == 0) {
                    c++;
                    n /= i;
                }
                res.put(i,c);
            }
        }
        return res;
    }

}