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 PYTHON3):

Solution:
from sys import stdin, stdout

def main():
    
    t = int(stdin.readline())
    for case in range(t):
        n = int(stdin.readline())
        a = stdin.readline()
        b = stdin.readline()
        k = 0
        seq = []
        flips = 0
        checks = n
        ax, ay, d = 0, n-1, 1
        by = n - 1
        while checks > 0:
            ch = a[ax]
            if flips % 2 == 1:
                if a[ax] == '1':
                    ch = '0'
                else:
                    ch = '1'
                    
            if ch == b[by]:
                k += 2
                seq.append(1)
            else:
                k += 1
            ax += d
            d *= -1
            ax, ay = ay, ax
            seq.append(checks)
            flips += 1
            checks -= 1
            by -= 1
                
        stdout.write(str(k))
        stdout.write(" ")
        stdout.write(" ".join(map(str, seq)))
        stdout.write("\n")
    return

if __name__ == '__main__':
    main()