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:
from functools import lru_cache
from sys import stdin, stdout
import sys
from math import *

# from collections import deque
# sys.setrecursionlimit(int(1e3))
# input = stdin.buffer.readline
# print = stdout.write

for __ in range(int(input())):
	n=int(input())
	a=list(input())
	b=list(input())
	same=0
	r=0
	x=0
	y1=n-1
	y2=n-1
	ans=[]
	while(y2>=0):
		# print(x,y1,y2,same,r)
		if(same==0):
			if(a[y1]==b[y2]):
				if(r==0):
					y1-=1
				else:
					y1+=1
				y2-=1
			else:
				if(a[y1]==a[x]):
					ans.append(abs(y1-x)+1)
					if(r==0):
						temp=x
						x=y1
						y1=temp+1
					else:
						temp=y1
						y1=x-1
						x=temp
					y2-=1
					same^=1
					r^=1
				else:
					ans.append(1)
					a[x]=a[y1]
		else:
			if(a[y1]!=b[y2]):
				if(r==0):
					y1-=1
				else:
					y1+=1
				y2-=1
			else:
				if(a[y1]==a[x]):
					ans.append(abs(y1-x)+1)
					if(r==0):
						temp=x
						x=y1
						y1=temp+1
					else:
						temp=y1
						y1=x-1
						x=temp
					y2-=1
					same^=1
					r^=1
				else:
					ans.append(1)
					# if(a[x]=="0"):
						# a[x]="1"
					# else:
						# a[x]="0"
					a[x]=a[y1]
	if(len(ans)==0):
		print(0)
	else:
		print(len(ans),end=" ")
		print(*ans)