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 cal(n, flip):
    if flip&1:
        return n^1
    else:
        return n

def cal_first():
    global p1, p2
    if p1 > p2:
        return first_arr2[p2]
    else:
        return first_arr[p1]

def inc_first():
    global p1, p2
    if p1 == p2:
        p1 += 1
    else:
        if p1<p2:
            p1 += 1
        else:
            p2 += 1

for i in range(int(input())):
    n = int(input())
    s1 = [int(i) for i in input()]
    s2 = [int(i) for i in input()]
    flip = 0
    ans = []
    first_arr = list(range(n))
    first_arr2 = list(range(n))[::-1]
    p1 = 0
    p2 = 0
    for ind in range(len(s2)-1, -1, -1):  
        first = cal_first()
        if cal(s1[first], flip) == s2[ind]:
            ans.append(1)
            s1[first]^=1
            ans.append(ind+1)
        else:
            ans.append(ind+1)
        flip += 1
        
        inc_first()

    

    if ans:
        print(len(ans), end = " ")
        print(*ans)
    else:
        print(0)