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;
char a[100005], b[100005];
int ans[200005];
char change(char s, int inv) {
  if (inv == 1) return s;
  if (s == '0') return '1';
  return '0';
}
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    int n;
    scanf("%d", &n);
    scanf("%s", a + 1);
    scanf("%s", b + 1);
    int tot = 0;
    int s = n;
    int t = 1;
    int inv = 1;
    for (int i = n; i >= 1; i--) {
      if (b[i] == change(a[s], inv)) {
        s -= inv;
        continue;
      }
      if (change(a[t], inv) == b[i]) {
        ans[++tot] = 1;
      }
      t += inv;
      int temp = t;
      t = s;
      s = temp;
      inv *= -1;
      ans[++tot] = i;
    }
    printf("%d ", tot);
    for (int i = 1; i <= tot; i++) printf("%d ", ans[i]);
    printf("\n");
  }
  return 0;
}