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 sys, os.path
from collections import deque
from fractions import Fraction as f
def IO():
    if os.path.exists('input.txt'):
        sys.stdin = open('input.txt', 'r')
        sys.stdout = open('output.txt', 'w')
    else:
        input=sys.stdin.readline
        print=sys.stdout.write
def nextInt():
    return int(input())
def nextTuple():
    return [int(a) for a in input().split()]
def nextArray():
    return list(map(int, input().split()))
def nextLine():
    return input()
def nextStringArray():
    return list(input().split())
IO()

'''code starts here'''


t=nextInt()
for _ in range(t):
    sb=[]
    n=nextInt()
    a=list(nextLine())
    b=list(nextLine())
    ptr=n-1
    operation_done=0
    operation_size=0
    for i in range(n):
        if operation_done%2==0:
            who=0+operation_done//2
        else:
            who=0+operation_done//2
            who=who+operation_size
        now=a[who]
        if operation_done%2!=0:
            if now=='0':
                now='1'
            else:
                now='0'
        if b[ptr]==now:
            sb.append("1")
        if True:
            sb.append(str(ptr+1))
            operation_done+=1
            operation_size=ptr
        ptr-=1
    print(len(sb),end=" ")
    print(" ".join(sb),end="")
    print()