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:
a = input()
for x in range(int(a)):
    b = input()
    c = input()
    d = input()
    list1 = [int(i) for i in c]
    list2 = [int(i) for i in d]
    ans = 0
    ans_list = []
    tag = len(list1)-1
    while(list1!=list2 and tag>=0):
        if(list1[tag]!=list2[tag]):
            if(list1[0]!=list1[tag]):
                if(list1[0]==1):
                    list1[0]=0
                else:
                    list1[0] = 1
                ans+=1
                ans_list.append(1)
            ans+=1
            ans_list.append(tag+1)
            for i in range(tag+1):
                if(list1[i]==0):
                    list1[i]=1
                else:
                    list1[i]=0
            list1 = list1[0:tag+1][::-1] + list1[tag+1:]       
        tag-=1
    if(ans==0):
        print(ans)
    else:
        print(ans,end=" ")
    for i in range(len(ans_list)):
        if(i!=len(ans_list)-1):
            print(ans_list[i],end=" ")
        else:
            print(ans_list[i])