#include <bits/stdc++.h>
using namespace std;
int t, n, i, nr, st, sp, si, val;
char ch;
vector<int> ans;
int a[100005];
int b[100005];
void upd(int r) {
  nr++;
  swap(sp, si);
  si += r;
}
int fval(int i) {
  int ans;
  if (nr % 2 == 0) {
    ans = sp - si + i;
    ans = a[ans];
  } else {
    ans = si - sp - i + 1;
    ans = a[ans] ^ 1;
  }
  return ans;
}
int main() {
  cin >> t;
  while (t) {
    t--;
    cin >> n;
    for (i = 1; i <= n; i++) {
      cin >> ch;
      a[i] = ch - '0';
    }
    for (i = 1; i <= n; i++) {
      cin >> ch;
      b[i] = ch - '0';
    }
    sp = si = 0;
    st = a[1];
    nr = 0;
    ans.clear();
    for (i = n; i >= 1; i--) {
      val = fval(i);
      if (val == b[i]) continue;
      if (st != val) {
        ans.push_back(1);
        st ^= 1;
      }
      ans.push_back(i);
      st ^= 1;
      upd(i);
    }
    cout << ans.size() << ' ';
    for (int it : ans) cout << it << ' ';
    cout << '\n';
  }
  return 0;
}

### 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 t, n, i, nr, st, sp, si, val;
char ch;
vector<int> ans;
int a[100005];
int b[100005];
void upd(int r) {
  nr++;
  swap(sp, si);
  si += r;
}
int fval(int i) {
  int ans;
  if (nr % 2 == 0) {
    ans = sp - si + i;
    ans = a[ans];
  } else {
    ans = si - sp - i + 1;
    ans = a[ans] ^ 1;
  }
  return ans;
}
int main() {
  cin >> t;
  while (t) {
    t--;
    cin >> n;
    for (i = 1; i <= n; i++) {
      cin >> ch;
      a[i] = ch - '0';
    }
    for (i = 1; i <= n; i++) {
      cin >> ch;
      b[i] = ch - '0';
    }
    sp = si = 0;
    st = a[1];
    nr = 0;
    ans.clear();
    for (i = n; i >= 1; i--) {
      val = fval(i);
      if (val == b[i]) continue;
      if (st != val) {
        ans.push_back(1);
        st ^= 1;
      }
      ans.push_back(i);
      st ^= 1;
      upd(i);
    }
    cout << ans.size() << ' ';
    for (int it : ans) cout << it << ' ';
    cout << '\n';
  }
  return 0;
}

```