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;
using LL = long long;
using LD = long double;
using ULL = unsigned long long;
using VI = vector<int>;
using VLL = vector<long long>;
using VULL = vector<unsigned long long>;
using VS = vector<string>;
using VB = vector<bool>;
using VC = vector<char>;
using PII = pair<int, int>;
using PLL = pair<long long, long long>;
using VPII = vector<pair<int, int>>;
using VPLL = vector<pair<long long, long long>>;
using VPULL = vector<pair<unsigned long long, unsigned long long>>;
using VVI = vector<vector<int>>;
using VVLL = vector<vector<long long>>;
using MII = map<int, int>;
using MLL = map<long long, long long>;
using SLL = set<long long>;
using SI = set<int>;
using PQI = priority_queue<int>;
template <class T>
T maxT(T a, T b) {
  return (a > b ? a : b);
}
template <class T>
T minT(T a, T b) {
  return (a < b ? a : b);
}
template <class T>
void setmax(T &a, T b) {
  a = (a > b ? a : b);
}
template <class T>
void setmin(T &a, T b) {
  a = (a < b ? a : b);
}
void fileio() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
  freopen("debug.txt", "w", stderr);
}
void ofileio() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
void clock_out() {
  cerr << "\nTime Elapsed : " << 1.0 * clock() / CLOCKS_PER_SEC << " s\n";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << H;
  debug_out(T...);
}
template <typename... Args>
void readln(Args &...args) {
  ((cin >> args), ...);
}
template <typename... Args>
void writeln(Args... args) {
  ((cout << args << " "), ...);
}
const LL MOD = 1000000007;
const LL SIZE = 10000005;
const int INF = 0x3f3f3f3f;
const LL LL_INF = 0x3f3f3f3f3f3f3f3f;
const LD PI = acos(-1);
const LL MAXN = numeric_limits<LL>::max();
LL n, x, y;
VLL mp(SIZE, -1);
LL dp(LL ln) {
  if (ln == 0LL) {
    return 0;
  } else if (ln == 1) {
    return x;
  } else {
    if (mp[ln] != -1) {
      return mp[ln];
    }
    LL val;
    if (ln % 2 == 0) {
      val = min(dp(ln - 1) + x, dp(ln / 2) + y);
    } else {
      val = min(dp(ln - 1) + x, dp((ln + 1) / 2) + x + y);
    }
    mp[ln] = val;
    return val;
  }
}
void solve() {
  cin >> n >> x >> y;
  cout << dp(n);
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
  srand(time(NULL));
  1;
  LL t = 1;
  while (t--) {
    solve();
  }
  1;
  return 0;
}