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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e5;
int ans;
int res[2 * MAX + 5];
char a[MAX + 5], b[MAX + 5];
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    int N;
    scanf("%d", &N);
    getchar();
    scanf("%s%s", a + 1, b + 1);
    for (int i = 1; i <= N; i++) {
      a[i] = a[i] - '0';
      b[i] = b[i] - '0';
    }
    ans = 0;
    for (int i = N; i > 0; i--) {
      if (i < N) {
        int k = N - i;
        if (k & 1)
          a[1] = !a[i + 1 + k / 2];
        else
          a[1] = a[1 + k / 2];
      }
      if (!((a[1]) ^ (b[i]))) res[ans++] = 1;
      res[ans++] = i;
    }
    printf("%d%c", ans, ans ? ' ' : '\n');
    for (int i = 0; i < ans; i++)
      printf("%d%c", res[i], i == ans - 1 ? '\n' : ' ');
  }
  return 0;
}