#include <bits/stdc++.h>
using namespace std;
const int maxn = 100000 + 5;
int n, a[maxn], b[maxn];
vector<int> ans;
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    ans.clear();
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) scanf("%1d", &a[i]);
    for (int i = 1; i <= n; ++i) scanf("%1d", &b[i]);
    int delta = 0, len = n, L = 1, R = n;
    bool dir = 0;
    while (len) {
      if (dir) {
        int op = a[L] ^ delta;
        if (op != b[len]) {
          if (a[L] == a[R]) {
            dir ^= 1, delta ^= 1;
          } else {
            a[R] ^= 1;
            ans.push_back(1);
            dir ^= 1, delta ^= 1;
          }
          ans.push_back(len);
          --R;
        } else {
          ++L;
        }
      } else {
        int op = a[R] ^ delta;
        if (op != b[len]) {
          if (a[R] == a[L]) {
            dir ^= 1, delta ^= 1;
          } else {
            a[L] ^= 1;
            ans.push_back(1);
            dir ^= 1, delta ^= 1;
          }
          ans.push_back(len);
          ++L;
        } else {
          --R;
        }
      }
      --len;
    }
    printf("%d ", ans.size());
    for (int i = 0; i < ans.size(); ++i) printf("%d ", ans[i]);
    puts("");
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
const int maxn = 100000 + 5;
int n, a[maxn], b[maxn];
vector<int> ans;
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    ans.clear();
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) scanf("%1d", &a[i]);
    for (int i = 1; i <= n; ++i) scanf("%1d", &b[i]);
    int delta = 0, len = n, L = 1, R = n;
    bool dir = 0;
    while (len) {
      if (dir) {
        int op = a[L] ^ delta;
        if (op != b[len]) {
          if (a[L] == a[R]) {
            dir ^= 1, delta ^= 1;
          } else {
            a[R] ^= 1;
            ans.push_back(1);
            dir ^= 1, delta ^= 1;
          }
          ans.push_back(len);
          --R;
        } else {
          ++L;
        }
      } else {
        int op = a[R] ^ delta;
        if (op != b[len]) {
          if (a[R] == a[L]) {
            dir ^= 1, delta ^= 1;
          } else {
            a[L] ^= 1;
            ans.push_back(1);
            dir ^= 1, delta ^= 1;
          }
          ans.push_back(len);
          ++L;
        } else {
          --R;
        }
      }
      --len;
    }
    printf("%d ", ans.size());
    for (int i = 0; i < ans.size(); ++i) printf("%d ", ans[i]);
    puts("");
  }
  return 0;
}

```