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.math.BigDecimal;
import java.text.CollationElementIterator;
import java.util.*;
import java.lang.*;

public class Main implements Runnable {
    public static void main(String[] args) {
        new Thread(null, new Main(), "Check2", 1 << 28).start();// to increse stack size in java
    }
    // CandidateCode
    static long mod = (long) (1e9 + 7);
    public void run() {
        InputReader in = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);

        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            int a[] = new int[n];
            int b[] = new int[n];
            int tmp[] = new int[n];
            for (int i=0;i<n;i++){
                a[i] = in.nextInt();
                tmp[i] = a[i];
            }
            Set <Integer> set = new HashSet<>();
            for (int i=0;i<n;i++){
                b[i] = in.nextInt();
                set.add(b[i]);
            }

            if (set.size() == 2){
                w.println("Yes");
            }
            else{
                boolean pos = true;
                for (int i=1;i<n;i++)if (a[i] < a[i-1])pos = false;
                if (pos)w.println("Yes");
                else w.println("No");
            }
        }
        w.close();
    }
    void debug(Object...args) {
        System.out.println(Arrays.deepToString(args));
    }
    long modinv(long a,long b) {
        long p=power(b,mod-2,mod);
        p=a%mod*p%mod;
        p%=mod;
        return p;
    }
    long power(long x,long y,long mod){
        if(y==0)return 1%mod;
        if(y==1)return x%mod;
        long res=1;
        x=x%mod;
        while(y>0)
        {
            if((y%2)!=0){
                res=(res*x)%mod;
            }
            y=y/2;
            x=(x*x)%mod;
        }
        return res;
    }
    long gcd(long a,long b){

        if(b==0)return a;
        return gcd(b,a%b);
    }
    void sev(int a[],int n){

        for(int i=2;i<=n;i++)a[i]=i;
        for(int i=2;i<=n;i++){

            if(a[i]!=0){
                for(int j=2*i;j<=n;){

                    a[j]=0;
                    j=j+i;
                }
            }

        }

    }
    static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars){
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String stock = "";
            try
            {
                stock = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return stock;
        }
        public int nextInt()
        {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-')
            {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do
            {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return readString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
}