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())
    s1 = list(input())
    s2 = list(input())

    i = n - 1
    ans = []
    count=0
    while s1 != s2:
        if count%2==0:
            if s2[-1] == s1[-1]:
                s1.pop()
                s2.pop()
            else:

                if s2[-1] == s1[0]:

                    ans.append(1)
                    if s1[0] == "0":

                        s1[0] = "1"

                    else:

                        s1[0] = "0"

                ans.append(len(s1))

                for i in range(len(s1)):
                    if s1[i] == "0":
                        s1[i] = "1"
                    else:
                        s1[i] = "0"

                s1 = s1[::-1]
                s1.pop()
                s2.pop()
        else:
            if s2[-1] != s1[-1]:
                s1.pop()
                s2.pop()
            else:

                if s2[-1] == s1[0]:

                    ans.append(1)
                    if s1[0] == "0":

                        s1[0] = "1"

                    else:

                        s1[0] = "0"

                ans.append(len(s1))

                for i in range(len(s1)):
                    if s1[i] == "0":
                        s1[i] = "1"
                    else:
                        s1[i] = "0"

                s1 = s1[::-1]
                s1.pop()
                s2.pop()


    print(len(ans), *ans)

    # i = n-1
    # n = n-1
    # ans=[]
    # while s1!=s2:
    #     print("n",s1[n],s2[n])
    #     if s1[n]==s2[n]:
    #         n-=1
    #     else:
    #         index=-1
    #         for i in range(1,n):
    #             if s1[i]==s1[0]:
    #                 index=i
    #                 break
    #
    #         for i in range(index+1):
    #             if s1[i]=="0":
    #                 s1[i]="1"
    #             else:
    #                 s1[i]="0"
    #         print(s1)
    #         ans.append(index+1)
    #         for i in range((index+1)//2):
    #             s1[i],s1[index-i]=s1[index-i],s1[i]
    #         ans.append(n)
    #         for i in range(n+1):
    #             if s1[i]=="0":
    #                 s1[i]="1"
    #             else:
    #                 s1[i]="0"
    #         print(s1)
    #         for i in range((n+1)//2):
    #             print("POP",s1)
    #             s1[i],s1[n-i]=s1[n-i],s1[i]
    #             print("lop",s1)
    #         print(s1)
    # print(ans)

    t -= 1