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 flip(arr,index):
    for i in range(index+1):
        if arr[i] == '0':
            arr[i] = '1'
        else:
            arr[i] = '0'
    for i in range((index+1)//2):
        arr[i], arr[index-i] = arr[index-i],arr[i]
    
T = int(input())
while T > 0:
    n = int(input())
    arr1 = list(input())
    arr2 = list(input())
    k = 0
    index = n-1
    res = []
    while index >= 0:
        if arr1[index] != arr2[index]:
            k += 1
            res.append(index+1)
            flip(arr1, index)
            if arr1[index] != arr2[index]:
                le = 1
                while True:
                    equal = True
                    for x in range(le):
                        if arr1[x] != arr2[index-le+x+1]:
                            equal = False
                            break
                    if equal is True:
                        le += 1
                    else:
                        break
                le -= 1
                flip(arr1, le-1)
                res.append(le)
                flip(arr1,index)
                res.append(index+1)
                k += 2
        else:
            index -= 1
    res.insert(0,k)
    print(*res)
    T -= 1