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 math import *
from collections import *
from random import *
from bisect import *
import sys
input=sys.stdin.readline
d={'1':'0','0':'1'}
t=int(input())
while(t):
    t-=1
    n=int(input())
    a=input().rstrip("\n")
    b=input().rstrip("\n")
    a=list(a)
    b=list(b)
    r=[]
    lp=n-1
    ch=n-1
    fp=0
    tu=0
    while(ch>=0):
        #print(r)
        if(tu%2==0):
            if(a[lp]==b[ch]):
                lp-=1
                ch-=1
                continue
            if(a[fp]==b[ch]):
                r.append(1)
                a[fp]=d[a[fp]]
                continue
        else:
            if(d[a[lp]]==b[ch]):
                lp+=1
                ch-=1
                continue
            if(d[a[fp]]==b[ch]):
                r.append(1)
                a[fp]=d[a[fp]]
                continue
        if(tu%2==0):
                r.append(ch+1)
                tu+=1
                fp,lp=lp,fp+1
        else:
                r.append(ch+1)
                tu+=1
                fp,lp=lp,fp-1
        ch-=1
    print(len(r),end=" ")
    print(*r)