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 math
t = int(input())
rez = []


def rev(a, n):
    l = 0
    r = n
    for j in range(n+1):
        if a[j] == "0":
            a[j] = "1"
        else:
            a[j] = "0"
    while l < r:
        buf = a[l]
        a[l] = a[r]
        a[r] = buf
        l+=1
        r-=1
    return a


for i in range(t):
    n = int(input())
    A = input()
    B = input()
    a = []
    b = []
    for j in range(n):
        a.append(A[j])
        b.append(B[j])
    k = 0
    m = n-1
    p = ""
    while m>0:
        if a[m] == b[m]:
            m -=1
        else:
            if a[0] == b[m]:
                k += 2
                p += "1 "
                p += str(m+1)+" "
                a = rev(a, 0)
                a = rev(a, m)
            else:
                k += 1
                p += str(m+1) + " "
                a = rev(a, m)
            m -= 1
    if a[0] != b[0]:
        k+=1
        p+="1 "
    rez.append(str(k)+" "+p)





for i in range(len(rez)):
    print(rez[i])