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:
//package codeforces.problem.nov;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/*
https://codeforces.com/problemset/problem/1381/A1
 */
public class TaskA1_1381 {

    static void swap(char[] arr, int pos) {
        for (int i = 0; i <= pos; i++) {
            if (arr[i] == '1') {
                arr[i] = '0';
            } else {
                arr[i] = '1';
            }
        }

        if (pos > 0) {
            for (int i = 0; i <= pos / 2; i++) {
                char tmp = arr[i];
                arr[i] = arr[pos - i];
                arr[pos - i] = tmp;
            }
        }
    }

    static void solve() {
        int n = FS.nextInt();
        String a = FS.next();
        String b = FS.next();

        List<Integer> ans = new ArrayList<>();
        char[] arr = a.toCharArray();

        int r = n - 1;
        while (!String.valueOf(arr).equals(b) && r >= 0) {
            if(arr[r] != b.charAt(r)) {
                if (arr[0] != b.charAt(r)) {
                    swap(arr, r);
                    ans.add(r + 1);
                } else {
                    swap(arr, 0);
                    ans.add(1);

                    swap(arr, r);
                    ans.add(r + 1);
                }
            }
            r--;
        }
        if (String.valueOf(arr).equals(b)) {
            FS.pt.print(ans.size() + " ");
            for (int i = 0; i < ans.size(); i++) {
                FS.pt.print(ans.get(i) + " ");
            }
        } else {
            FS.pt.print(0);
        }
        FS.pt.println();
    }

    public static void main(String[] args) {
        int T = FS.nextInt();
        for (int tt = 0; tt < T; tt++) {
            solve();
        }
        FS.pt.close();
    }

    static class FS {
        private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private static StringTokenizer st = new StringTokenizer("");
        static PrintWriter pt = new PrintWriter(System.out);

        static String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        static int nextInt() {
            return Integer.parseInt(next());
        }

        static int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        static int[][] read2Array(int m, int n) {
            int[][] a = new int[m][n];
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    a[i][j] = nextInt();
                }
            }
            return a;
        }

        static long[][] read2ArrayL(int m, int n) {
            long[][] a = new long[m][n];
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    a[i][j] = nextInt();
                }
            }
            return a;
        }

        void printArr(long[] arr) {
            for (long value : arr) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static long[] readArrayL(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        static void printArr(int[] arr) {
            for (int value : arr) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static void printArrL(int[] arr) {
            for (int value : arr) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static void print2Arr(int[][] arr, int m, int n) {
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    pt.print(arr[i][j]);
                    pt.print(" ");
                }
                pt.println();
            }
            pt.println();
        }

        static void print2Arr(long[][] arr, int m, int n) {
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    pt.print(arr[i][j]);
                    pt.print(" ");
                }
                pt.println();
            }
            pt.println();
        }

        static List<Long> readListLong(int n) {
            List<Long> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        static List<Integer> readListInt(int n) {
            List<Integer> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }

        static <T> void printList(List<T> list) {
            for (T value : list) {
                pt.print(value);
                pt.print(" ");
            }
            pt.println();
        }

        static void close() {
            pt.close();
        }

        static long nextLong() {
            return Long.parseLong(next());
        }
    }
}