#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int T;
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    string a, b;
    cin >> a >> b;
    vector<int> ret;
    int reverse = 0;
    char first = a[0];
    int l = 0, r = n - 1;
    for (int i = n - 1; i >= 1; --i) {
      int cur = l + i;
      if (reverse) {
        cur = r - i;
      }
      if (a[cur] == b[i] && reverse == 0) {
        r--;
        continue;
      }
      if (a[cur] != b[i] && reverse == 1) {
        l++;
        continue;
      }
      if (first != b[i]) {
        ret.push_back(i + 1);
      } else {
        ret.push_back(1);
        ret.push_back(i + 1);
      }
      if (reverse == 0) {
        l++;
      } else {
        r--;
      }
      reverse = 1 - reverse;
      first = b[i];
    }
    if (first != b[0]) {
      ret.push_back(1);
    }
    cout << ret.size();
    for (auto i = 0; i < ret.size(); ++i) {
      cout << " " << ret[i];
    }
    cout << endl;
  }
}

### Prompt

Generate a cpp solution to 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() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int T;
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    string a, b;
    cin >> a >> b;
    vector<int> ret;
    int reverse = 0;
    char first = a[0];
    int l = 0, r = n - 1;
    for (int i = n - 1; i >= 1; --i) {
      int cur = l + i;
      if (reverse) {
        cur = r - i;
      }
      if (a[cur] == b[i] && reverse == 0) {
        r--;
        continue;
      }
      if (a[cur] != b[i] && reverse == 1) {
        l++;
        continue;
      }
      if (first != b[i]) {
        ret.push_back(i + 1);
      } else {
        ret.push_back(1);
        ret.push_back(i + 1);
      }
      if (reverse == 0) {
        l++;
      } else {
        r--;
      }
      reverse = 1 - reverse;
      first = b[i];
    }
    if (first != b[0]) {
      ret.push_back(1);
    }
    cout << ret.size();
    for (auto i = 0; i < ret.size(); ++i) {
      cout << " " << ret[i];
    }
    cout << endl;
  }
}

```