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 io,os
from collections import deque
#input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
RL = lambda : list(map(int, input().split(' ')))
def flip(a):
    if a=='1':
        b = '0'
        return b
    b = '1'
    return b
T = int(input())
for _ in range(T):
    n = int(input())
    a = input()
    b = input()
    flag = 0
    ind1 = 1
    ind2 = n-1
    ind = n-1
    i = n-1
    cnt = 0
    first = a[0]
    ans = []
    while ind1<ind2:
        if flag==0:
            ind = ind2
            ind2-=1
        else:
            ind = ind1
            ind1+=1
        #print(ind)
        if cnt%2:
            toch = flip(a[ind])
        else:
            toch = a[ind]
        if toch!=b[i]:
            #print(toch,first,ind)
            if toch!=first:
                ans.append(1)
            ans.append(i+1)
            first = flip(toch)
            if flag==0:
                flag=1
            else:
                flag = 0
            cnt+=1
        i-=1
    
    
    if flag==0:
            ind = ind2
            ind2-=1
    else:
        ind = ind1
        ind1+=1
    if cnt%2:
        toch = flip(a[ind])
    else:
        toch = a[ind]
    if toch!=b[i]:
        if toch!=first:
            ans.append(1)
        ans.append(i+1)
        first = flip(toch)
    if first!=b[0]:
        ans.append(1)
    print(len(ans),end=' ')
    print(*ans)