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;
void flip(string& a, long int j, bool& zero, bool& one) {
  long int i = 0;
  while (i < j) {
    a[i] = (a[i] == '0' ? '1' : '0');
    a[j] = (a[j] == '0' ? '1' : '0');
    swap(a[i], a[j]);
    i++;
    j--;
  }
  if (i == j) {
    a[i] = (a[i] == '0' ? '1' : '0');
  }
  return;
}
int main() {
  long int t;
  cin >> t;
  while (t--) {
    long int n;
    cin >> n;
    string a, b;
    cin >> a >> b;
    vector<long int> res;
    bool f, r;
    long int e;
    e = 0, f = false, r = false;
    for (long int i = n - 1; i > -1; i--) {
      char Ai, A0;
      if (r) {
        long int index = e - i;
        if (a[index] == '0') {
          if (f)
            Ai = '1';
          else
            Ai = '0';
        } else {
          if (f)
            Ai = '0';
          else
            Ai = '1';
        }
        index = e - 0;
        if (a[index] == '0') {
          if (f)
            A0 = '1';
          else
            A0 = '0';
        } else {
          if (f)
            A0 = '0';
          else
            A0 = '1';
        }
      } else {
        long int index = e + i;
        if (a[index] == '0') {
          if (f)
            Ai = '1';
          else
            Ai = '0';
        } else {
          if (f)
            Ai = '0';
          else
            Ai = '1';
        }
        index = e + 0;
        if (a[index] == '0') {
          if (f)
            A0 = '1';
          else
            A0 = '0';
        } else {
          if (f)
            A0 = '0';
          else
            A0 = '1';
        }
      }
      if (Ai == b[i]) continue;
      if (b[i] != A0) {
        res.push_back(i + 1);
        if (r)
          e = e - i;
        else
          e = e + i;
        r = !r;
        f = !f;
      } else {
        res.push_back(1);
        res.push_back(i + 1);
        if (r)
          e = e - i;
        else
          e = e + i;
        r = !r;
        f = !f;
      }
    }
    if (!res.size()) {
      cout << 0 << endl;
      continue;
    }
    cout << res.size() << ' ';
    for (long int x : res) cout << x << ' ';
    cout << endl;
  }
}