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,math
from collections import deque,defaultdict
import operator as op
from functools import reduce

#sys.setrecursionlimit(10**6) 

I=sys.stdin.readline

 #s="abcdefghijklmnopqrstuvwxyz"

"""
x_move=[-1,0,1,0,-1,1,1,-1]
y_move=[0,1,0,-1,1,1,-1,-1]
"""
def ii():
	return int(I().strip())
def li():
	return list(map(int,I().strip().split()))
def mi():
	return map(int,I().strip().split())

"""def ncr(n, r):
    r = min(r, n-r)
    numer = (reduce(op.mul, range(n, n-r, -1), 1))%(10**9+7)
    denom = (reduce(op.mul, range(1, r+1), 1))%(10**9+7)
    return (numer // denom)%(10**9+7)"""
def ncr(n, r, p):
    # initialize numerator
    # and denominator
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, 
            p - 2, p)) % p
 

def gcd(x, y):
    while y:
        x, y = y, x % y
    return x

def valid(row,col,rows,cols,rcross,lcross):
 	return rows[row]==0 and cols[col]==0 and rcross[col+row]==0 and lcross[col-row]==0


def div(n):
	tmp=[]
	for i in range(2,int(n**.5)+1):
		if n%i==0:
			cnt=0
			while(n%i==0):
				n=n//i 
				cnt+=1
			tmp.append((i,cnt))
	if n>1:
		tmp.append((n,1))
	return tmp

def isPrime(n):
	if n<=1:
		return False
	elif n<=2:
		return True
	else:
		flag=True
		for i in range(2,int(n**.5)+1):
			if n%i==0:
				flag=False
				break
		return flag

def s(b):
	d=defaultdict(int)
	while b>0:
		tmp=b%10
		if d[tmp]>0:
			return False
		d[tmp]=1
		b=b//10
	return True

def main():
	#ans=""
	for _ in range(ii()):
		n=ii()
		s=I().strip()
		s2=I().strip()
		ans=[]
		for i in range(1,n):
			if s[i]!=s[i-1]:
				ans.append(i)

		if s[n-1]=='1':
			ans.append(n)
		tmp=[]
		for i in range(1,n):
			if s2[i]!=s2[i-1]:
				tmp.append(i)

		if s2[n-1]=='1':
			tmp.append(n)

		ans+=tmp[::-1]
		ans=[len(ans)]+ans

		print(*ans)







	#print(ans)



	
		




	










	


	

	

		



		

		
		


	
	

		
	

		




		




			












			
		
			



		


	
			
						
			








	





			
		



	
			





	

























	
	
	





if __name__ == '__main__':
	main()