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
import sys
tt = int(input())

for loop in range(tt):

    n = int(input())

    a = input()
    b = input()

    if n == None:
        if a[0] == b[0]:
            print (0)
        else:
            print (1,1)
        sys.exit()

    ind = [None] * n
    tmp = 0
    for i in range(n-1,-1,-2):
        ind[i] = tmp
        tmp += 1
    if n % 2 == 0:
        for i in range(0,n,2):
            ind[i] = tmp
            tmp += 1
    else:
        for i in range(1,n,2):
            ind[i] = tmp
            tmp += 1

    #print (*ind)

    ans = []
    x = 0
    for i in range(n-1,-1,-1):

        if x == 0 and b[i] == a[ind[i]]:
            ans.append(1)
        elif x == 1 and b[i] != a[ind[i]]:
            ans.append(1)
        ans.append(i+1)
        x ^= 1

    print (len(ans),*ans)