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:
import collections
t1=int(input())
for _ in range(t1):
  flipflag=0
  bitflag=0
  n=int(input())
  a2=input()
  a=collections.deque([])
  for i in range(n):
    a.append(a2[i])
  b=input()
  ans=[]
  for i in range(n-1,-1,-1):
    if flipflag==0:
      p=a[-1]
    else:
      p=a[0]
    if bitflag==1:
      if p=='0':
        p='1'
      else:
        p='0'
    if flipflag==0:
      q=a[0]
    else:
      q=a[-1]
    if bitflag==1:
      if q=='0':
        q='1'
      else:
        q='0'
    if p!=b[i]:
      if q!=b[i]:
        ans.append(str(i+1))
        if flipflag==0:
          a.popleft()
        else:
          a.pop()
        flipflag=1-flipflag
        bitflag=1-bitflag
      else:
        ans.append('1')
        ans.append(str(i+1))
        if flipflag==0:
          a.popleft()
        else:
          a.pop()
        flipflag=1-flipflag
        bitflag=1-bitflag
    else:
      if flipflag==0:
        a.pop()
      else:
        a.popleft()
  print(len(ans))
  if len(ans)>0:
    print(' '.join(ans))