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
import math
import heapq
import collections
def inputnum():
    return(int(input()))
def inputnums():
    return(map(int,input().split()))
def inputlist():
    return(list(map(int,input().split())))
def inputstring():
    return([x for x in input()])
def inputmatrixchar(rows):
    arr2d = [[j for j in input().strip()] for i in range(rows)] 
    return arr2d
def inputmatrixint(rows):
    arr2d = []
    for _ in range(rows):
        arr2d.append([int(i) for i in input().split()])
    return arr2d
    
t=int(input())
for q in range(t):
    n = inputnum()
    a = inputstring()
    b = inputstring()
    ansa = []
    one = False
    for i in range(n):
        if not one and a[i] == '1':
            one = True
            if i != 0:
                ansa.append(i)
        if i == n-1 and a[i] == '1':
            ansa.append(i+1)
        if one and a[i] == '0':
            one = False
            ansa.append(i)
    ansb = []
    one = False
    for i in range(n):
        if not one and b[i] == '1':
            one = True
            if i != 0:
                ansb.append(i)
        if i == n-1 and b[i] == '1':
            ansb.append(i+1)
        if one and b[i] == '0':
            one = False
            ansb.append(i)
    print(len(ansa) + len(ansb), end = ' ')
    for i in range(len(ansa)):
        print(ansa[i], end = ' ')
    for i in reversed(range(len(ansb))):
        print(ansb[i], end = ' ')
    print()