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:
def main():
    t = int(input())
    for i in range(t):
        n = int(input())
        str1 = input()
        str2 = input()
        anslist = []
        if str1 == str2:
            print(0)
        else:
            for j in range(n):
                if str1[0] == str2[-j-1]:
                    anslist.append(1)
                anslist.append(n - j)
                tmpstr = ''
                for k in range(0, n - j):
                    if str1[k] == '0':
                        tmpstr +='1'
                    else:
                        tmpstr += '0'
                if len(tmpstr)>1:
                    tmpstr = str2[-j-1] + tmpstr[1:]
                    # print(str2[-1],tmpstr[1:])
                else:
                    tmpstr = str2[-1]
                # print(tmpstr)
                str1 = tmpstr[::-1] + str1[n-j:]
                # print(str1)
            print(len(anslist), end=' ')
            for j in range(len(anslist)-1):
                print(anslist[j], end=' ')
            print(anslist[len(anslist) - 1])

        # li = []
        # for j in range(m):
        #     a, b = map(int, input().split())
        #     li.append([a, b])
        # l1 = sorted(li, key=lambda x: x[0], reverse=1)
        # l2 = sorted(li, key=lambda x: x[1], reverse=1)
        # print(l1)
        # print(l2)
        # if i < t-1:
        #     aaaa = input()

if __name__ == '__main__':
    main()