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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Task710E {

    public static void main(String[] args) throws IOException{
        InputScanner is = new InputScanner();
        int n = is.nextInt();
        int x = is.nextInt(); // insert or delete
        int y = is.nextInt(); // copy the content of text file

        long[] time = new long[n+1];
        time[1] = x;
        for (int i = 2; i <=n ; i++) {
            time[i] = i%2==0 ? Math.min(time[i-1]+x, time[(i+1)/2] + y) : Math.min(time[i-1]+x, time[(i+1)/2]+x+y);
        }
        System.out.println(time[n]);
    }

    static class InputScanner {
        BufferedReader br;
        StringTokenizer st;

        public InputScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }

        public long nextLong() throws IOException {
            String next = next();
            return Long.parseLong(next);
        }
    }
}