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:
import sys
input = sys.stdin.buffer.readline

def main():

    t = int(input())
    for _ in range(t):
        n = int(input())
        a = list(str(input()))
        b = list(str(input()))

        a = a[2:-3]
        b = b[2:-3]

        #print(a)
        #print(b)

        def func(x, cnt):
            if (cnt+1)%2 == 0:
                return x
            else:
                return str(1-int(x))


        ans = []
        cnt = 0
        for i in reversed(range(n)):
            if b[i] != a[0]:
                ans.append(i+1)
                if i%2 == (n-1)%2:
                    a[0] = func(a[n-1-cnt//2], cnt)
                else:
                    a[0] = func(a[1+cnt//2], cnt)
                    #print(a)
            else:
                ans.append(1)
                a[0] = str(1-int(a[0]))
                #print(a)
                ans.append(i+1)
                if i%2 == (n-1)%2:
                    a[0] = func(a[n-1-cnt//2], cnt)
                else:
                    a[0] = func(a[1+cnt//2], cnt)
            cnt += 1
            #print(a[0])

        #print(*ans)
        ans = [len(ans)]+ans
        print(*ans)

if __name__ == '__main__':
    main()