Problem: zscoder wants to generate an input file for some programming competition problem.

His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.

Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.

zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.

Input

The only line contains three integers n, x and y (1 ≤ n ≤ 107, 1 ≤ x, y ≤ 109) — the number of letters 'a' in the input file and the parameters from the problem statement.

Output

Print the only integer t — the minimum amount of time needed to generate the input file.

Examples

Input

8 1 1


Output

4


Input

8 1 10


Output

8

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int64_t seed;
mt19937 rng(seed = chrono::steady_clock::now().time_since_epoch().count());
inline int64_t rnd(int64_t l = 0, int64_t r = numeric_limits<int64_t>::max()) {
  return uniform_int_distribution<int64_t>(l, r)(rng);
}
template <typename T, typename G>
ostream& operator<<(ostream& out, const pair<T, G>& a) {
  return out << "( " << a.first << ", " << a.second << ")";
}
template <typename T>
ostream& operator<<(ostream& out, const vector<T>& a) {
  out << "[ ";
  for (const auto& i : a) out << i << ", ";
  return out << "]" << endl;
}
template <typename T>
ostream& operator<<(ostream& out, const set<T>& a) {
  out << "{ ";
  for (const auto& i : a) out << i << ", ";
  return out << "}" << endl;
}
template <typename T, typename G>
ostream& operator<<(ostream& out, const map<T, G>& a) {
  out << "< ";
  for (const auto& i : a) out << i << ", ";
  return out << ">" << endl;
}
template <typename T, size_t N>
typename enable_if<!is_same<typename remove_cv<T>::type, char>::value,
                   ostream&>::type
operator<<(ostream& out, T (&a)[N]) {
  out << "[ ";
  for (const auto& i : a) out << i << ", ";
  return out << "]" << endl;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << (H) << ' ';
  debug_out(T...);
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int64_t n, first, second;
  cin >> n >> first >> second;
  vector<int64_t> a(n + 1);
  a[0] = 0;
  for (int64_t i = 1; i <= n; ++i) a[i] = a[i - 1] + first;
  for (int64_t i = 1; i <= n; ++i) {
    a[i] = min(a[i], a[i / 2] + second + (i & 1) * first);
    a[i] = min(a[i], a[(i + 1) / 2] + second + (i & 1) * first);
  }
  cout << a[n] << '\n';
  return 0;
}