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 t;
int n;
string a, b;
char inv(char c) { return ((c == '0') ? '1' : '0'); }
bool inver;
char Get(int i) {
  if (inver)
    return inv(a[i]);
  else
    return a[i];
}
int main() {
  cin >> t;
  while (t--) {
    cin >> n;
    cin >> a;
    cin >> b;
    vector<int> ans;
    int ar = n - 1;
    inver = false;
    char af = a[0];
    for (int i = 0; i < n; ++i) {
      if (Get(ar) == b[n - 1 - i]) {
        if (inver)
          ar++;
        else
          ar--;
        continue;
      }
      if (af != b[n - 1 - i]) {
        ans.push_back(n - i);
        char tmp = Get(ar);
        if (inver) {
          ar += (n - 1 - i);
        } else {
          ar -= (n - 1 - i);
        }
        inver = !inver;
        if (inver) {
          ++ar;
        } else {
          --ar;
        }
        af = inv(tmp);
      } else {
        ans.push_back(1);
        ans.push_back(n - i);
        char tmp = Get(ar);
        if (inver) {
          ar += (n - 1 - i);
        } else {
          ar -= (n - 1 - i);
        }
        inver = !inver;
        if (inver) {
          ++ar;
        } else {
          --ar;
        }
        af = inv(tmp);
      }
    }
    cout << (int)ans.size() << " ";
    for (int pre : ans) cout << pre << " ";
    cout << endl;
  }
}