#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
long long posx[] = {1, -1, 0, 0};
long long posy[] = {0, 0, 1, -1};
void solve() {
  long long n, i, j, k;
  string a, b;
  cin >> n >> a >> b;
  vector<long long> v;
  int x1 = 0, x2 = n - 1;
  bool f = 0;
  for (i = n - 1; i >= 0; i--) {
    if (f == 0) {
      if (a[x1] == b[i]) {
        v.push_back(1);
      }
      v.push_back(x2 - x1 + 1);
      x1++;
      f = 1;
    } else {
      if (a[x2] != b[i]) v.push_back(1);
      v.push_back(x2 - x1 + 1);
      x2--;
      f = 0;
    }
  }
  cout << v.size() << " ";
  for (auto x : v) cout << x << " ";
  cout << '\n';
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
long long posx[] = {1, -1, 0, 0};
long long posy[] = {0, 0, 1, -1};
void solve() {
  long long n, i, j, k;
  string a, b;
  cin >> n >> a >> b;
  vector<long long> v;
  int x1 = 0, x2 = n - 1;
  bool f = 0;
  for (i = n - 1; i >= 0; i--) {
    if (f == 0) {
      if (a[x1] == b[i]) {
        v.push_back(1);
      }
      v.push_back(x2 - x1 + 1);
      x1++;
      f = 1;
    } else {
      if (a[x2] != b[i]) v.push_back(1);
      v.push_back(x2 - x1 + 1);
      x2--;
      f = 0;
    }
  }
  cout << v.size() << " ";
  for (auto x : v) cout << x << " ";
  cout << '\n';
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

```