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.util.*;
import java.io.*;
import java.math.*;
public class Main{
	static long mod = (long)(1e9+7);
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String sp[])throws IOException{
		Scanner sc = new Scanner(System.in);
		//FastReader sc = new FastReader();	
		int t = sc.nextInt();
		while(t-->0){
			int n = sc.nextInt();
			String s1 = sc.next();
			String s2 = sc.next();
			ArrayList<Integer> al = new ArrayList<>();
			if(s1.equals(s2)){
				System.out.println("0");
				continue;
			}
			if(n==1){
				if(!s1.equals(s2)){
					System.out.println("1 1");
				}else System.out.println("0");
				continue;
			}
			ArrayList<Integer> two = new ArrayList<>();
			for(int i=0;i<n-1;i++){
				if(s1.charAt(i)!=s1.charAt(i+1)){
					two.add(i+1);
				}
			}
			if(s1.charAt(n-1)=='1')
				two.add(n);
			if(s2.charAt(n-1)=='1')
				two.add(n);
			int siz = two.size();
			for(int i=n-2;i>=0;i--){
				if(s2.charAt(i)!=s2.charAt(i+1)){
					two.add(i+1);
				}
			}
			StringBuilder sb = new StringBuilder();
			for(int val : two)
				sb.append(val+" ");
			System.out.println(two.size()+" "+sb.toString());
		}
	}
	
	public static int[] convert(int ind, int arr1[]){
		int n = arr1.length;
		int temp[] = new int[n];
		for(int i=0;i<n;i++){
			temp[i]=arr1[i];
		}
		
		int y = 0;
		for(int i=ind;i>=0;i--){
			temp[i] = 1-arr1[y];
			y++;
		}
		return temp;
	}
	
	public static ArrayList<Integer> primefactor(int n){
		int sqrt = (int)Math.sqrt(n);
		ArrayList<Integer> al = new ArrayList<>();
		while(n%2==0){
			al.add(2);
			n/=2;
		}
		for(int i=3;i<=sqrt;i+=2){
			while(n%i==0){
				al.add(i);
				n/=i;
			}
		}
		if(n>2)
			al.add(n);
		return al;
	}
	
	public static long sum(long val){
		long fg =0 ;
		while(val!=0){
			fg+=val%10;
			val/=10;
		}
		return fg;
	}
	
	
	
	public static ArrayList<Integer> factor(int n){
		int sqrt = (int)Math.sqrt(n);
		ArrayList<Integer> al = new ArrayList<>();
		for(int i=1;i<=sqrt;i++){
			if(n%i!=0)
				continue;
			int first = i;
			int second = n/i;
			al.add(i);
			if(first==second){
				continue;
			}
			al.add(n/i);
		}
		return al;
	}
	
	public static long power(long x, long y) 
	{ 
		long temp; 
		if( y == 0) 
			return 1l; 
		temp = power(x, y/2); 
		if (y%2 == 0) 
			return (temp*temp)%mod; 
		else
			return ((x*temp)%mod*temp)%mod; 
	} 
	
	public static ArrayList<Integer> comp(){
		ArrayList<Integer> al = new ArrayList<>();
			int n = (int)2e5;
			boolean arr[] = new boolean[n+1];
			int sqrt = (int)Math.sqrt(n);
			for(int i=2;i<=sqrt;i++){
				if(arr[i]==false){
					for(int j=i*i;j<=n;j+=i){
						arr[j]=true;
					}
				}
			}
			for(int i=2;i<=n;i++){
				if(arr[i]==false)
					al.add(i);
			}
			
		return al;
	}
	
	public static class pair{
		int x;
		int y;
		pair(int x, int y){
			this.x=x;
			this.y=y;
		}
	}
	
	public static class comp implements Comparator<pair>{
		public int compare(pair o1, pair o2){
			if(o1.y==o2.y)
				return o1.x-o2.x;
			return o1.y-o2.y;
		}
	}
	
	
	static class Node{
		int node;
		int d;
		ArrayList<Integer> al = new ArrayList<>();	
	}
	

	static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }
	
		
	static class FastReader 
	{ 
		final private int BUFFER_SIZE = 1 << 16; 
		private DataInputStream din; 
		private byte[] buffer; 
		private int bufferPointer, bytesRead; 
  
		public FastReader() 
		{ 
			din = new DataInputStream(System.in); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public FastReader(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 ni() 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(); 
		} 
	} 
}