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.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static int mod = 1000000007;
	static long inf = (long) 1e16;
	static int[] l, r;
	static int n, m, k;
	static long all, ans;
	static HashSet<Integer>[] ad;
	static int[][] memo;
	static long[] f;
	static ArrayList<Integer> h;
	static boolean vis[];
	static int[] dist;
	static int INF = Integer.MAX_VALUE;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			char[] a = sc.nextLine().toCharArray();
			char[] b = sc.nextLine().toCharArray();
			int k = 0;
			sb = new StringBuilder();
			for (int i = n - 1; i >= 0; i--) {
				if (a[i] == b[i])
					continue;
				if (a[i] != a[0]) {
					k += 2;
					sb.append(1 + " ");
					sb.append((i + 1) + " ");
					if (a[0] == '1')
						a[0] = '0';
					else
						a[0] = '1';
				} else {
					k++;
					sb.append((i + 1) + " ");
				}
				int id = 0;
				int j = i;
				while (id <= j) {
					if (id == j) {
						if (a[j] == '0')
							a[j] = '1';
						else
							a[j] = '0';
						break;
					}
					char tem = a[id];
					if (a[j] == '0')
						a[id] = '1';
					else
						a[id] = '0';
					if (tem == '0')
						a[j] = '1';
					else
						a[j] = '0';
					j--;
					id++;
				}
			}
			out.println(k + " " + sb);
		}
		out.flush();
	}

	static class pair implements Comparable<pair> {
		int x;
		int y;

		pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public String toString() {
			return x + " " + y;
		}

		@Override
		public int compareTo(pair o) {
			if (y == o.y)
				return x - o.x;
			return o.y - y;
		}

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public int[] nextArrInt(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextArrLong(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}