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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

/**
 * @project: Codeforces658
 * @author: izhanatuly
 * @date: 21/07/2020
 */
public class C2 {
    static Scanner scanner;

    public static void main(String[] args) {
        scanner = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int cases = scanner.nextInt();
        for (int t = 0; t < cases; t++) {
            runTestCase();
        }
    }

    public static void runTestCase() {
        int n = scanner.nextInt();
        String Astr = scanner.next();
        String Bstr = scanner.next();
        char[] A = Astr.toCharArray();
        char[] B = Bstr.toCharArray();
        boolean reversed = false;
        List<Integer> res = new ArrayList<>();
        int i=0;
        int R = n-1;
        int L = 0;
        for (int j = n - 1; j > 0; j--) {
            int index = reversed ? L : R;
            char a = reversed ? reverse(A[index]) : A[index];
            char b = B[j];
            int firstIndex = reversed ? R : L;
            if (a == b) {
                // pass
            } else if (A[L] == A[R]) {
                // one operation
                res.add(j+1);
                reversed = !reversed;
//                Astr = inverse(Astr, j+1);
            } else {
                // 2 operations
                res.add(1);
                A[firstIndex] = reverse(A[firstIndex]);
                res.add(j+1);
                reversed = !reversed;

//                Astr = inverse(Astr, 1);
//                Astr = inverse(Astr, j+1);
            }
//            System.out.println(Astr + " " + j);
            if(reversed) {
                L++;
            } else {
                R--;
            }
        }
        char firstChar = reversed ? reverse(A[R]) : A[R];
        if(firstChar != B[0]) {
            res.add(1);
//            Astr = inverse(Astr, 1);
        }
        System.out.print(res.size() + " ");
        for(int num : res) {
            System.out.print(num + " ");
        }
        System.out.println();
//        System.out.println(Astr);
//        System.out.println(Bstr);
    }

    static char reverse(char c) {
        char res = c=='1' ? '0' : '1';
        return res;
    }

//    static String inverse(String a, int len) {
//        char[] res = a.toCharArray();
//        int i=0;
//        int j=len-1;
//        for(int k=0; k<len; k++) {
//            res[k] = res[k]=='1' ? '0' : '1';
//        }
//        while(i<j) {
//            char temp = res[i];
//            res[i] = res[j];
//            res[j] = temp;
//            i++;
//            j--;
//        }
//        return new String(res);
//    }
}