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:
for _ in range(int(input())):
    n = int(input())
    A = input()
    B = input()
    A = [int(i) for i in A]
    B = [int(i) for i in B]
    k = 0
    ans = []
    cnt = n-1
    fp = False
    for i in range(n-1,-1,-1):
        # print(i,cnt,fp)
        if(fp):
            if(A[cnt-i]!=B[i]):
                continue
            else:
                if(A[cnt]==A[cnt-i]):
                    k+=1
                    ans.append(i)
                    fp = False
                    cnt-=1
                else:
                    k+=1
                    ans.append(0)
                    if(i>0):
                        k+=1
                        ans.append(i)
                        fp = False  
                        cnt-=1                
        else:
            if(A[cnt]==B[i]):
                cnt-=1
                continue
            else:
                if(A[cnt]==A[cnt-i]):
                    k+=1
                    ans.append(i)
                    fp = True
                else:
                    k+=1
                    ans.append(0)
                    if(i>0):
                        k+=1
                        ans.append(i)
                        fp = True
    print(k,end=" ")
    for i in ans:
        print(i+1, end=" ")
    print()
    # for j in ans:
    #     x = A[0:j+1]
    #     # print("x",x)
    #     x = [1-i for i in x]
    #     K = []
    #     for i in range(j,-1,-1):
    #         K.append(x[i])
    #     # print("K",K)
    #     K.extend(A[j+1:])
    #     A = K.copy()
    #     print("A",j+1,A)
    # print("A",A)
    # print("B",B)