Problem: This is the easy 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 3n 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≤ 1000) — 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 1000.

Output

For each test case, output an integer k (0≤ k≤ 3n), 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 100100;
string Read() {
  static char Buffer[N];
  scanf("%s", Buffer);
  return Buffer;
}
int main() {
  int T;
  cin >> T;
  while (T--) {
    int n;
    scanf("%d", &n);
    string a = Read();
    string b = Read();
    for (char& c : a) c -= '0';
    for (char& c : b) c -= '0';
    deque<char> dq;
    for (char c : a) dq.push_back(c);
    int Suff = 0;
    bool Rev = false;
    vector<int> Ans;
    for (int i = n - 1; ~i; --i) {
      if (!Rev) {
        if ((dq.back() ^ Suff) != b[i]) {
          if ((dq.front() ^ Suff) == b[i]) {
            Ans.push_back(0);
            dq.front() ^= 1;
          }
          Suff ^= 1;
          Rev ^= true;
          Ans.push_back(i);
        }
      } else {
        if ((dq.front() ^ Suff) != b[i]) {
          if ((dq.back() ^ Suff) == b[i]) {
            Ans.push_back(0);
            dq.back() ^= 1;
          }
          Suff ^= 1;
          Rev ^= true;
          Ans.push_back(i);
        }
      }
      if (!Rev) {
        dq.pop_back();
      } else {
        dq.pop_front();
      }
    }
    printf("%d", int(Ans.size()));
    for (int x : Ans) printf(" %d", x + 1);
    puts("");
  }
}