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,m=map(int,input().split())
    l1=list(map(int,input().split()))
    l2=list(map(int,input().split()))
    f=0
    for i in range(n):
        if l1[i] in l2:
            f=1
            ans=l1[i]
            break
    if(f==0):
        print("NO")
    else:
        print("YES")
        print(1, ans)"""
"""for _ in range(int(input())):
    n=int(input())
    l=list(map(int,input().split()))
    x=l.count(1)
    if(x==0):
        print("First")
    else:
        if(x==n):
            if(n%2==0):
                print("Second")
            else:
                print("First")
        else:
            c=0
            for i in range(n):
                if(l[i]==1):
                    c+=1
                else:
                    break
            if(c%2==0):
                print("First")
            else:
                print("Second")"""
for _ in range(int(input())):
    n=int(input())
    la=str(input())
    lb=str(input())
    ans=n
    l=[]
    a=list(la)
    b=list(lb)
    left=0
    right=n-1
    for i in range(n-1,-1,-1):
        temp=n-i+1
        if(temp%2==0):
            if(a[left]==b[i]):
                l.append(1)
            left+=1
            l.append(i+1)
        else:
            if(a[right]!=b[i]):
                l.append(1)
            right-=1
            l.append(i+1)


    print(len(l),end=" ")
    for i in range(len(l)):
        print(l[i],end=" ")
    print()