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:
def trailone(l):
    c=0
    for i in l:
        if i==1:
            c+=1
        else:
            break
    return c
def inp():
    return(int(input()))
def insr():
    s = input()
    return s
def inlt():
    return(list(map(int,input().split())))
def convert(a,b):
    
    s1=0
    e1=len(b)-1
    rev=0
    ans=[]
    for i in range(len(a)-1,-1,-1):
#         print(a,s1,e1,rev)
        if rev!=1:
            if a[e1]==b[i]:
                e1-=1
                continue
            elif a[s1]==b[i]:
                ans.append(0+1)
                ans.append(i+1)
                s1+=1
                rev=1
            else:
                ans.append(i+1)
                s1+=1
                rev=1
                
        else:
            if a[s1]!=b[i]:
                s1+=1
                continue
            elif a[e1]!=b[i]:
                ans.append(0+1)
                ans.append(i+1)
                e1-=1
                rev=0
            else:
                ans.append(i+1)
                e1-=1
                rev=0
#         print(a,s1,e1,rev)
    return ans
if __name__ == "__main__":
    r=inp()
    for i in range(r):
        l2=inlt()
        a=insr()
        b=insr()
        ans=convert(a,b)
        if len(ans)==0:
            print("0\n")
        else:
            print(str(len(ans))+" "+" ".join([str(i) for i in ans])+"\n")