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:



t = int(input())
while t!=0:
    n = int(input())
    a = list(input())
    b = list(input())
    ans = []

    st = 0
    en = n-1
    inv_f = drn_f = 0
    count = 0
    j = n-1
    while count<n:
        count+=1
        if inv_f==0:
            if drn_f==0:
                if a[en]==b[j]:
                    en-=1
                    j-=1
                    pass
                else:
                    if a[st]!=b[j]:
                        ans.append(j)
                        st+=1
                        inv_f=1
                        drn_f=1
                        j-=1
                    else:
                        ans.append(0)
                        ans.append(j)
                        st+=1
                        inv_f=1
                        drn_f=1
                        j-=1
            else:
                if a[st]==b[j]:
                    st+=1
                    j-=1
                else:
                    if a[en]!=b[j]:
                        ans.append(j)
                        en-=1
                        j-=1
                        inv_f=1
                        drn_f=0
                    else:
                        ans.append(0)
                        ans.append(j)
                        en-=1
                        j-=1
                        inv_f=1
                        drn_f=0
        else:
            if drn_f == 0:
                if a[en] != b[j]:
                    en -= 1
                    j -= 1
                    pass
                else:
                    if a[st] == b[j]:
                        ans.append(j)
                        st += 1
                        inv_f = 0
                        drn_f = 1
                        j -= 1
                    else:
                        ans.append(0)
                        ans.append(j)
                        st += 1
                        inv_f = 0
                        drn_f = 1
                        j -= 1
            else:
                if a[st] != b[j]:
                    st += 1
                    j -= 1
                else:
                    if a[en] == b[j]:
                        ans.append(j)
                        en -= 1
                        j -= 1
                        inv_f = 0
                        drn_f = 0
                    else:
                        ans.append(0)
                        ans.append(j)
                        en -= 1
                        j -= 1
                        inv_f = 0
                        drn_f = 0


    print(len(ans),end=" ")
    for i in range(len(ans)):
        print(ans[i]+1,end=" ")

    print()


    t-=1