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 reverse_sublist(lst,start,end):
    lst[start:end] = lst[start:end][::-1]
    return lst
def found(lst,start,end):
    lst[start:end] = lst[start:end][::-1]
    return lst
def invertion(arr, prefix,dp):
    tmp="".join(map(str,arr[0:prefix]))

    if(tmp in dp):
        arr[0:prefix]=dp[tmp]
    else:
        for i in range(prefix):
            if(arr[i]==0):
                arr[i]=1
            else:
                arr[i]=0
        arr=reverse_sublist(arr,0,prefix)
        dp.update({tmp:arr[0:prefix]})

def main():
    t = int(input())
    dp = {}
    for _ in range(t):
        n =int(input())
        a = list(map(int,input()))
        b = list(map(int,input()))
        arr = []
        i=0
        for i in range(0,n):
            if(not a[i] == b[i]):
                # if(i==0):
                #     arr.append(1)
                #     invertion(a,i+1,dp)
                # else:    
                    arr.append(i+1)
                    invertion(a,i+1,dp)
                    arr.append(1)
                    invertion(a,1,dp)
                    arr.append(i+1)
                    invertion(a,i+1,dp)


            # while not a[0:i] == b[0:i]:
                # if(j==1):
                #     j=i
                # else:
                #     j-=1

        # while(not a == b):
        #     if(i==0):
        #         i=n-1
        #     invertion(a,i,dp)
        #     i-=1
        # print(*arr)
        print(len(arr),*arr)

main()