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 long long MOD = 1e9 + 7;
const long long INF = 1e9 + 7;
vector<long long> ans;
void solve(string& a, string& b, long long idx, long long start, long long end,
           bool flip) {
  if (idx < 0) return;
  if (start == end) {
    if (a[start] == b[idx]) {
      if (flip) ans.push_back(1);
    } else {
      if (!flip) ans.push_back(1);
    }
    return;
  }
  if (start <= end) {
    if (flip) {
      if (a[end] != b[idx]) {
        solve(a, b, idx - 1, start, end - 1, flip);
      } else {
        if (a[start] != b[idx]) ans.push_back(1);
        ans.push_back(idx + 1);
        solve(a, b, idx - 1, end, start + 1, !flip);
      }
    } else {
      if (a[end] == b[idx]) {
        solve(a, b, idx - 1, start, end - 1, flip);
      } else {
        if (a[start] == b[idx]) ans.push_back(1);
        ans.push_back(idx + 1);
        solve(a, b, idx - 1, end, start + 1, !flip);
      }
    }
  } else {
    if (flip) {
      if (a[end] != b[idx]) {
        solve(a, b, idx - 1, start, end + 1, flip);
      } else {
        if (a[start] != b[idx]) ans.push_back(1);
        ans.push_back(idx + 1);
        solve(a, b, idx - 1, end, start - 1, !flip);
      }
    } else {
      if (a[end] == b[idx]) {
        solve(a, b, idx - 1, start, end + 1, flip);
      } else {
        if (a[start] == b[idx]) ans.push_back(1);
        ans.push_back(idx + 1);
        solve(a, b, idx - 1, end, start - 1, !flip);
      }
    }
  }
}
void solve() {
  ans.clear();
  long long n;
  cin >> n;
  string a, b;
  cin >> a >> b;
  solve(a, b, n - 1, 0, n - 1, false);
  cout << ans.size() << " ";
  for (long long& e : ans) cout << e << " ";
  cout << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t = 1;
  cin >> t;
  for (long long i = 1; i <= t; i++) {
    solve();
  }
  return 0;
}