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 PYTHON):

Solution:
import atexit, io, sys 

  
# A stream implementation using an in-memory bytes  
# buffer. It inherits BufferedIOBase. 

buffer = io.BytesIO() 

sys.stdout = buffer

  
# print via here 

@atexit.register 

def write(): 

    sys.__stdout__.write(buffer.getvalue()) 
def ab(x):
    if x>0:
        return x
    return -x
for _ in range(input()):
    
   
    n=input();
    a=raw_input();b=raw_input()
    a=[int(i) for i in a]
    b=[int(i) for i in b]
    v=[]
    head=0;tail=n-1
    co=0
    for i in range(n-1,-1,-1):
        if a[tail]^co!=b[i]:
            if head!=tail:
                if a[tail]!=a[head]:
                    v.append(1)
                    a[head]^=1
                co^=1
                v.append(ab(head-tail)+1)
                if head>tail:
                    tail,head=head-1,tail
                    
                else:
                    tail,head=head+1,tail
                
                
                
                
  
                
               
            else:
                v.append(1)
        
        else:
            if head<tail:
                tail-=1
            elif head>tail:
                tail+=1
            else:
                break
        
    s=str(len(v))+" ";
    for i in v:
        s+=str(i);s+=" ";
    print s