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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;

public class Codeforces_648_div_2_1 {

	public static void main(String[] args) throws IOException {
		Reader rd = new Reader();
		int t = rd.nextInt() ;
		while(t-- > 0) {
			int n = rd.nextInt() ;
			int a[] = new int[n] ;
			int b[] = new int[n] ;
			boolean isIncreasing = true;
			int oneCount = 0 ;
			int zeroCount =0 ;
			a[0] = rd.nextInt() ;
			for(int i= 1 ;i< n ;i++) {
				a[i] = rd.nextInt() ;
				if(a[i] < a[i-1]) {
					isIncreasing = false ;
				}
			}
			
			for(int i = 0; i<n;i++) {
				b[i] = rd.nextInt() ;
				if(b[i] == 0) {
					zeroCount++ ;
				}else {
					oneCount++;
				}
			}
			if(isIncreasing) {
				System.out.println("Yes");
			}else if(zeroCount == 0 || oneCount == 0) {
				System.out.println("No");
			}else {
				System.out.println("Yes");
			}
			
		}

	}

	
/*
 * Problem 1
 */
//	public static void main(String[] args) throws IOException {
//		Reader rd = new Reader();
//		int t = rd.nextInt() ;
//		while(t-- > 0) {
//			int n = rd.nextInt() ;
//			int m = rd.nextInt() ;
//			Map<Integer, Boolean> rows = new HashMap<Integer, Boolean>() ;
//			Map<Integer, Boolean> cols = new HashMap<Integer, Boolean>() ;
//			
//			for(int i = 0 ; i< n ;i++) {
//				for(int j= 0 ; j< m ;j++) {
//					int v = rd.nextInt();
//					if(v == 1) {
//						rows.put(i, true) ;
//						cols.put(j, true) ;
//					}
//				}
//			}
//			int unfilled = Math.min(n-rows.size(), m-cols.size());
//			if(unfilled%2 == 0) {
//				System.out.println("Vivek") ;
//			}else {
//				System.out.println("Ashish") ;
//			}
//			
//			
//		}
//
//	}
	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(); 
        } 
    } 


}