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 os
import sys
#input = sys.stdin.buffer.readline
input = sys.stdin.readline
#sys.setrecursionlimit(int(3e5)) 
from collections import deque
from queue import PriorityQueue
import math
import copy
#  list(map(int, input().split()))
#####################################################################################


class AC(object):    
    def fan(self, s, pos):
        for i in range(pos+1):
            if(s[i] == '0'):
                s[i] = '1'
            else:
                s[i] = '0'
        pass

    def __init__(self):
        t = int(input())
        for _ in range(t):
            n = int(input())
            a = deque(input())
            if(len(a) > n):
                a.pop()
            b = list(input())
            ans = []
            now = 0
            sign = 0
            for pos in range(n)[::-1]:
                if(sign == 0):
                    if(b[pos] == a[now]):
                        ans.append(1)
                else:
                    if(b[pos] != a[now]):
                        ans.append(1)
                pass
                if(now == 0):
                    a.popleft()
                else:
                    a.pop()
                ans.append(pos+1)
                sign = 1-sign
                now = -1 - now                    
            pass
            print(len(ans), end = ' ')
            print(' '.join(map(str, ans)))
        pass


    def main(self):

        pass

if __name__ == "__main__":
    ac = AC()
    ac.main()
    pass