CodeForces710E Generate a String

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 nletters '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.

Example

Input

8 1 1

Output

4

Input

8 1 10

Output

8

f[i] : 生成i个字符需要的时间
如果i是奇数，分为复制后加一个和复制后删一个讨论以及从i-1加一个
如果i是偶数，分为复制和i-1加一个

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <map>
#include <set>
#include <vector>
#include <queue>
#include <cmath>

using namespace std;

const int N = 1e7 + 10;

unsigned long long f[N], n, x, y;

int main() {
    cin >> n >> x >> y;
    f[1] = x;
    for(unsigned long long i = 2 ; i <= n ; i ++) {
        if(i & 1) {
            f[i] = min(f[i - 1] + x, min(f[i / 2], f[i / 2 + 1]) + x + y);
        } else {
            f[i] = min(f[i - 1] + x, f[i / 2] + y);
        }
    }
    cout << f[n] << endl;
}