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.*;
import java.util.*;

import java.lang.*;
import java.math.*;

public class B {
	public void run() throws Exception {
		FastScanner sc = new FastScanner();
		
		int test = sc.nextInt();
		outer:
		for (int q = 0; q<test; q++) {
			int n = sc.nextInt();
			String a = sc.next();
			String b = sc.next();
			ArrayList<Integer> ind = new ArrayList<Integer>();
			boolean one = false;
			if (n == 1) {
				if (a.charAt(0) != b.charAt(0)) System.out.println(1 + " " + 1);
				else System.out.println(0);
			}
			else {
				if (a.charAt(1) == '1') one = true;
				for (int i = 0; i<n-1; i++) {
					if (a.charAt(i) != a.charAt(i+1)) {
						ind.add(i+1);
						if (a.charAt(i+1) == '1') one = true;
						else one = false;
					}
				}
				if (one) {
					ind.add(n);
					one = false;
				}
		//		System.out.println(ind);
				for (int i = n-2; i>=0; i--) {
					if (i == n-2) {
						if (b.charAt(i+1) != '0') {
				//			System.out.println((i+1) + " " + b.charAt(i+1));
							ind.add(i+2);
						}
					}
					if (b.charAt(i) != b.charAt(i+1)) {
						ind.add(i+1);
					}
					
				}
			//	System.out.println(a);
			//	System.out.println(b);
				System.out.print(ind.size() + " ");
				for (int i = 0; i<ind.size(); i++) {
					System.out.print(ind.get(i) + " ");
				}
				System.out.println();
			}
		}
	}
	//SSR <3 2020
	public class Pair implements Comparable<Pair>{
		int num, times;
		public Pair(int a, int b) {
			num = a;
			times = b;
		}
		public int compareTo(Pair a) {
			if (num == a.num) return times-a.times;
			return num-a.num;
		}
		public String toString() {
			return num + " " + times;
		}
	}
	public int[] shuffleArray(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
        	int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        return arr;
	}
	public boolean isPrime(long n) {
		for (long i = 2; i<=Math.sqrt(n); i++) {
			if (n%i == 0) return false;
		}
		return true;
	}
	public static long gcd(long a, long b)   {
		if (a == b) return a;
		if (a > b) return gcd(a-b, b);
		return gcd(a, b-a);
    }
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
 
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
 
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
 
		public int nextInt() {
			return Integer.parseInt(next());
		}
 
		public long nextLong() {
			return Long.parseLong(next());
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
 
	}
	public static void main (String[] args) throws Exception {
		new B().run();
	}
}