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.io.*;

public class Codeforces{
    // Input
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public String nextLine() {
            String s = null;
            try {
                s = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return s;
        }

        public String nextParagraph() {
            String line = null;
            String ans = "";
            try {
                while ((line = reader.readLine()) != null) {
                    ans += line;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return ans;
        }
    }
    //Template
    static int mod = 998244353;
    static void printArray(int ar[]){ for(int x:ar) System.out.print(x+" ");}
    static void printArray(ArrayList<Integer> ar){ for(int x:ar) System.out.print(x+" ");}
    static long gcd(long a, long b){ if (a == 0) return b; return gcd(b%a, a);}
    static long power(long x, long y, int p) { long res = 1; x = x % p;  while (y > 0) { if((y & 1)==1) res = (res * x) % p; y = y >> 1;x = (x * x) % p;  } return res;}
    static void takeArrayInput(InputReader sc, int ar[]){ for(int i=0;i<ar.length;i++) ar[i]=sc.nextInt(); }
    static void takeArrayInput(InputReader sc, long ar[]){ for(int i=0;i<ar.length;i++) ar[i]=sc.nextLong(); }
    static void take2dArrayInput(InputReader sc, int ar[][]){ for(int i=0;i<ar.length;i++) for(int j=0;j<ar[i].length;j++) ar[i][j]=sc.nextInt(); }
    static void take2dArrayInput(InputReader sc, long ar[][]){ for(int i=0;i<ar.length;i++) for(int j=0;j<ar[i].length;j++) ar[i][j]=sc.nextLong(); }
    static ArrayList<ArrayList<Integer>> graph(InputReader sc, int n, int m){
        ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();
        for(int i=0;i<n;i++) list.add(new ArrayList<Integer>());
        for(int i=0;i<m;i++){ int u = sc.nextInt(); int v = sc.nextInt(); list.get(u).add(v); list.get(v).add(u); }
        return list;
    }
    static void sieveOfEratosthenes(int n, ArrayList<Integer> pr) {
        // Create a boolean array "prime[0..n]" and initialize
        // all entries it as true. A value in prime[i] will
        // finally be false if i is Not a prime, else true.
        boolean prime[] = new boolean[n + 1];
        for (int i = 0; i < n; i++)
            prime[i] = true;
        for (int p = 2; p * p <= n; p++) {
            // If prime[p] is not changed, then it is a prime
            if (prime[p] == true) {
                // Update all multiples of p
                pr.add(p);
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }

    // Write code here
    static class Data {
        int val;
        int type;
        public Data(int val, int type) {
            this.type = type;
            this.val = val;
        }
    }

    public static void main(String args[]) {
        InputReader sc = new InputReader();
        PrintWriter pw = new PrintWriter(System.out);
        int t = sc.nextInt();
        int i = 0 , j=0;
        for (int z = 0; z < t; z++) {
            int n=sc.nextInt();
            boolean s = true, o = false;
            int ar[] = new int[n];
            int b[] = new int[n];
            for (i = 0 ; i < n; i++) {
                ar[i] = sc.nextInt();
            }
            for (i = 0 ; i < n; i++) {
                b[i] = sc.nextInt();
            }
            for (i = 1 ; i < n; i++) {
                if (ar[i] < ar[i-1]) {
                    s = false;
                }
                if (b[i] != b[i-1])
                    o = true;
            }
            // pw.println(s +" " +o);
            if (s || o) {
                pw.println("Yes");
            } else {
                pw.println("No");
            }
        }
        pw.close();
    }
}