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:
            cnt = 0
            tmp = 0
            while cnt < n:
                cnt += 1
                flag = 0
                if cnt%2==1:
                    flag = cnt//2
                else:
                    flag = -cnt//2
                if (tmp%2 == 0 and str1[flag] == str2[-cnt]) or (tmp%2==1 and str1[flag]!=str2[-cnt]):
                    anslist.append(1)
                    # tmp += 1
                anslist.append(n - cnt + 1)
                tmp += 1
            print(len(anslist), end=' ')
            for j in range(len(anslist)-1):
                print(anslist[j], end=' ')
            print(anslist[len(anslist) - 1])
            # 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()