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:
// Working program using Reader Class

import org.omg.Messaging.SYNC_WITH_TRANSPORT;

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.*;

public class Main1 {
    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++];
        }

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

    static class Hero {
        int pow, end;

        Hero(int a, int b) {
            pow = a;
            end = b;
        }
    }

    static class Tree {
        Tree left, right;
        int st, en, num;

        Tree(int a, int b, int c) {
            st = a;
            en = b;
            num = c;
        }
    }

    private static void upd(Tree tr, int pos, int val) {
        tr.num += val;
        if (tr.st == tr.en) {
            return;
        }
        int mid = (tr.st + tr.en) / 2;
        if (pos <= mid) {
            if (tr.left == null) {
                tr.left = new Tree(tr.st, mid, 0);
            }
            upd(tr.left, pos, val);
        } else {
            if (tr.right == null) {
                tr.right = new Tree(mid + 1, tr.en, 0);
            }
            upd(tr.right, pos, val);
        }
    }

    private static int query(Tree tr, int siz) {
        if (tr == null) {
            return 0;
        }
        tr.num--;
        if (tr.st == tr.en) {
            return tr.st;
        }
        if (tr.left == null) {
            return query(tr.right, siz);
        }
        if (tr.left.num >= siz) {
            return query(tr.left, siz);
        }
        return query(tr.right, siz - tr.left.num);
    }

    private static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    static int find(int a, int[] par) {
        if (par[a] == 0) {
            return a;
        }
        return par[a] = find(par[a], par);
    }

    static void union(int a, int b, int[] par, int[] rank) {
        if (rank[a] >= rank[b]) {
            par[b] = a;
            rank[a] += rank[b];
        } else {
            par[a] = b;
            rank[b] += rank[a];
        }
    }

    private static long gg(int a) {
        return (a * (a + 1L)) / 2L;
    }

    private static long gg(long a) {
        return (a * (a + 1L)) / 2L;
    }

    public static void main(String[] args) throws IOException {
        Reader z = new Reader();
        int t=z.nextInt();
        while(t-->0) {
            int n = z.nextInt(), i, p=0, q=0;
            int[] a = new int[n];
            int[] b = new int[n];
            for(i=0;i<n;i++){
                a[i]=z.nextInt();
            }
            for(i=0;i<n;i++){
                b[i]=z.nextInt();
                if(b[i]==0){
                    p=1;
                }
                else{
                    q=1;
                }
            }
            if(p==1 && q==1){
                System.out.println("Yes");
                continue;
            }
            for(i=1;i<n;i++){
                if(a[i]<a[i-1]){
                    break;
                }
            }
            System.out.println(i<n?"No":"Yes");
        }
        z.close();
    }
}