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>
std::mt19937 rng(
    (int)std::chrono::steady_clock::now().time_since_epoch().count());
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);
  int t;
  std::cin >> t;
  while (t--) {
    int n;
    std::string a, b;
    std::cin >> n >> a >> b;
    int l = 0, r = n - 1;
    int got = 0;
    std::vector<int> ans;
    for (int i = 0; i < n; i++) {
      int pos;
      if (i % 2 == 0)
        pos = l++;
      else
        pos = r--;
      int ch = a[pos] - '0';
      if ((ch + got) % 2 == b[n - i - 1] - '0') {
        ans.push_back(1);
      }
      ans.push_back(n - i);
      got ^= 1;
    }
    assert((int)ans.size() <= 2 * n);
    std::cout << ans.size() << '\n';
    for (int i = 0; i < (int)ans.size(); i++) {
      std::cout << ans[i] << (i + 1 == (int)ans.size() ? '\n' : ' ');
    }
    continue;
    for (auto x : ans) {
      for (int i = 0; i < x; i++) {
        a[i] = a[i] == '0' ? '1' : '0';
      }
      std::reverse(a.begin(), a.begin() + x);
    }
    std::cout << a << " should be " << b << '\n';
  }
}