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;
int main() {
  int i, j, k, c, x, y, z, n, m, t;
  cin >> t;
  string u, v;
  while (t--) {
    cin >> n;
    getline(cin, v);
    cin >> u >> v;
    z = 0;
    vector<int> h;
    int a[n + 2], b[n + 2];
    for (i = 0; i < n; i++) {
      a[i] = u[i] - '0';
      b[i] = v[i] - '0';
    }
    x = a[n - 1];
    y = 0;
    z = n;
    bool ans = true;
    for (i = n - 1; i > 0; i--) {
      if (ans) {
        ans = false;
        x = a[--z];
      } else {
        ans = true;
        x = a[++y] ^ 1;
      }
      if (x != b[i]) {
        if (x != a[0])
          h.push_back(1);
        else
          a[0] ^= 1;
      } else {
        if (x == a[0]) {
          h.push_back(1);
          a[0] ^= 1;
        }
      }
      h.push_back(i + 1);
    }
    if (a[0] != b[0]) h.push_back(1);
    cout << h.size();
    z = h.size();
    for (i = 0; i < z; i++) cout << " " << h[i];
    cout << endl;
  }
}