#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    string a, b;
    cin >> a >> b;
    if (a == b) {
      cout << 0 << endl;
    } else if (n == 1) {
      if (a[0] == b[0])
        cout << 0 << endl;
      else {
        cout << 1 << endl;
        cout << 1 << endl;
      }
    } else {
      vector<int> ans;
      int flip = 0;
      int index = 0;
      for (int i = n - 1; i >= 0; i--) {
        if (a[index] == b[i] && flip == 0) {
          ans.push_back(1);
        }
        if (a[index] != b[i] && flip == 1) {
          ans.push_back(1);
        }
        ans.push_back(i + 1);
        if (flip) {
          flip = 0;
          index -= i;
        } else {
          flip = 1;
          index += i;
        }
      }
      cout << ans.size() << endl;
      for (auto i = ans.begin(); i != ans.end(); i++) cout << *i << " ";
      ;
      cout << endl;
      ;
    }
  }
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

This is the hard 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 2n 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≤ 10^5) — 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 10^5.

Output

For each test case, output an integer k (0≤ k≤ 2n), 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    string a, b;
    cin >> a >> b;
    if (a == b) {
      cout << 0 << endl;
    } else if (n == 1) {
      if (a[0] == b[0])
        cout << 0 << endl;
      else {
        cout << 1 << endl;
        cout << 1 << endl;
      }
    } else {
      vector<int> ans;
      int flip = 0;
      int index = 0;
      for (int i = n - 1; i >= 0; i--) {
        if (a[index] == b[i] && flip == 0) {
          ans.push_back(1);
        }
        if (a[index] != b[i] && flip == 1) {
          ans.push_back(1);
        }
        ans.push_back(i + 1);
        if (flip) {
          flip = 0;
          index -= i;
        } else {
          flip = 1;
          index += i;
        }
      }
      cout << ans.size() << endl;
      for (auto i = ans.begin(); i != ans.end(); i++) cout << *i << " ";
      ;
      cout << endl;
      ;
    }
  }
  return 0;
}

```