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;
using ll = long long;
using vll = vector<ll>;
using ull = unsigned long long;
using int2 = pair<ll, ll>;
using int3 = tuple<ll, ll, ll>;
template <typename A>
string to_string(const A &v);
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(char c) { return string(1, c); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(const tuple<A, B, C> &p) {
  return "(" + to_string(std::get<0>(p)) + ", " + to_string(std::get<1>(p)) +
         ", " + to_string(std::get<2>(p)) + ")";
}
template <typename A>
string to_string(const A &v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename T>
void sort(vector<T> &val) {
  sort(val.begin(), val.end());
}
template <typename T>
void reverse(vector<T> &val) {
  reverse(val.begin(), val.end());
}
template <typename T>
void reverse(map<T, T> &val) {
  reverse(val.begin(), val.end());
}
template <typename T>
void sort_b(vector<T> &val) {
  sort(val.begin(), val.end(), greater<T>());
}
template <typename T>
T pair_sum(pair<T, T> &val) {
  return val.first + val.second;
}
template <typename T>
T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <typename T>
T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <typename T>
T mul_mod(T a, T b, T mod) {
  T res = 0;
  a %= mod;
  while (b) {
    if (b & 1) {
      res = (res + a) % mod;
    }
    a = (2 * a) % mod;
    b >>= 1;
  }
  return res;
}
template <typename T>
T fac_mod(T v, T mod) {
  ll res = 1;
  for (ll i = 1; i <= v; i++) {
    res *= i;
    res = res % mod;
  }
  return res;
}
template <typename T>
T pow_mod(T v, T p, T mod) {
  if (p == 1) return v;
  if (p % 2 == 0) {
    T t = pow_mod(v, p / 2, mod);
    return (t * t) % mod;
  } else {
    return (v * pow_mod(v, p - 1, mod)) % mod;
  }
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
class mytask {
 public:
  mytask() {}
  int solve() {
    ll t;
    cin >> t;
    while (t--) {
      ll n;
      cin >> n;
      string a, b;
      cin >> a >> b;
      vll s(n);
      vll p(n);
      for (ll i = 0; i < n; i++) {
        s[i] = a[i] - '0';
        p[i] = b[i] - '0';
      }
      ll reverse_count = 0;
      vll res;
      for (ll i = n - 1; i >= 0; i--) {
        if ((s[i] ^ reverse_count) == p[i]) continue;
        if (i > 0 && (s[0] ^ reverse_count) == p[i]) {
          res.push_back(1);
        }
        res.push_back(i + 1);
        ;
        ;
        reverse(s.begin(), s.begin() + i + 1);
        ;
        ;
        reverse_count ^= 1;
      }
      cout << res.size() << " ";
      for (ll v : res) cout << v << " ";
      cout << "\n";
    }
    return 0;
  }
};
int main() {
  auto task = mytask();
  task.solve();
  return 0;
}