Problem: This is the easy version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved.

There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix.

For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001.

Your task is to transform the string a into b in at most 3n operations. It can be proved that it is always possible.

Input

The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 3t lines contain descriptions of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 1000) — the length of the binary strings.

The next two lines contain two binary strings a and b of length n.

It is guaranteed that the sum of n across all test cases does not exceed 1000.

Output

For each test case, output an integer k (0≤ k≤ 3n), followed by k integers p_1,…,p_k (1≤ p_i≤ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation.

Example

Input


5
2
01
10
5
01011
11100
2
01
01
10
0110011011
1000110100
1
0
1


Output


3 1 2 1
6 5 2 5 3 1 2
0
9 4 1 2 10 4 1 2 1 5
1 1

Note

In the first test case, we have 01→ 11→ 00→ 10.

In the second test case, we have 01011→ 00101→ 11101→ 01000→ 10100→ 00100→ 11100.

In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged.

Solution (in JAVA):

Solution:
import java.io.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;

public class C2 {

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
	    PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	    
	    int t = sc.nextInt();
	    while(t-- > 0) {
	    	int n = sc.nextInt();
	    	char[] a = new char[n];
	    	char[] a_prime = new char[n];
	    	char[] b = new char[n];
	    	
	    	String s = sc.nextLine();
	    	for(int i = 0; i < n; i++) {
	    		a[i] = s.charAt(i);
	    		a_prime[i] = a[i] == '1' ? '0' : '1';
	    	}
	    	s = sc.nextLine();
	    	for(int i = 0; i < n; i++) {
	    		b[i] = s.charAt(i);
	    	}
	    		    	
	    	ArrayList<Integer> moves = new ArrayList<>();
	    	boolean reverse = false;
	    	// smaller index
	    	int start = 0;
	    	// larger index
	    	int end = n - 1;
	    	for(int i = n - 1; i >= 0; i--) {
	    		if(reverse) {
	    			if(a_prime[end] == b[i])
	    				moves.add(1);
	    			
	    			moves.add(i + 1);
	    			end--;
	    		}else {
	    			if(a[start] == b[i])
	    				moves.add(1);
	    			
	    			moves.add(i + 1);
	    			
	    			start++;
	    		}
	    		
	    		reverse = !reverse;
	    	}
	    	
	    	out.print(moves.size() + " ");
	    	for(int move : moves) {
	    		out.print(move + " ");
	    	}
	    	out.println();    	
	    }
	    
	    out.close();
	}
	
	private static class FastScanner {
        private int BS = 1<<16;
        private char NC = (char)0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;
 
        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }
 
        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            }
            catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }
 
        private char getChar(){
            while(bId==size) {
                try {
                    size = in.read(buf);
                }catch(Exception e) {
                    return NC;
                }
                if(size==-1)return NC;
                bId=0;
            }
            return (char)buf[bId++];
        }
 
        public int nextInt() {
            return (int)nextLong();
        }
 
        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }
 
        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }
 
        public long nextLong() {
            cnt=1;
            boolean neg = false;
            if(c==NC)c=getChar();
            for(;(c<'0' || c>'9'); c = getChar()) {
                if(c=='-')neg=true;
            }
            long res = 0;
            for(; c>='0' && c <='9'; c=getChar()) {
                res = (res<<3)+(res<<1)+c-'0';
                cnt*=10;
            }
            return neg?-res:res;
        }
 
        public double nextDouble() {
            double cur = nextLong();
            return c!='.' ? cur:cur+nextLong()/cnt;
        }
 
        public String next() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c>32) {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }
 
        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c!='\n') {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }
 
        public boolean hasNext() {
            if(c>32)return true;
            while(true) {
                c=getChar();
                if(c==NC)return false;
                else if(c>32)return true;
            }
        }
    }
}