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:
#!/usr/bin/env python3

import sys
input=sys.stdin.readline

t=int(input())
for _ in range(t):
    n=int(input())
    a=list(input())
    b=list(input())
    ans=[]
    l=0
    r=n-1
    for i in range(n-1,-1,-1):
        if a[i]!=b[i]:
            r=i
            break
    else:
        r=0
    if l==r:
        if a[0]==b[0]:
            print(0)
        else:
            print(1,1)
        continue
    else:
        flip=False
        count=r
        while l!=r:
            if flip==False:
                if a[l]==b[count]:
                    if a[l]=='0':
                        a[l]='1'
                    else:
                        a[l]='0'
                    ans.append(1)
                    ans.append(count+1)
                else:
                    ans.append(count+1)
                flip=True
            else:
                if a[r]!=b[count]:
                    if a[r]=='0':
                        a[r]='1'
                    else:
                        a[r]='0'
                    ans.append(1)
                    ans.append(count+1)
                else:
                    ans.append(count+1)
                flip=False
            for i in range(count,-1,-1):
                if flip==True:
                    if a[l+count-i]==b[i]:
                        l=l+count-i
                        count=i
                        break
                else:
                    if a[r-count+i]!=b[i]:
                        r=r-count+i
                        count=i
                        break
            else:
                if flip==False:
                    l=r
                else:
                    r=l
        if flip==False:
            if a[l]!=b[0]:
                ans.append(1)
        else:
            if a[r]==b[0]:
                ans.append(1)
        ans=[len(ans)]+ans
        print(*ans)