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:
/**
 * Created by ankeet on 8/22/16.
 */
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class E710 {

    static FastReader in = null;
    static PrintWriter out = null;



    public static void solve()
    {
        int n = in.nint();
        long x = in.nint();
        long y = in.nint();
        long[] dp = new long[n+1];
        dp[1] = x;
        for(int i=2; i<=n; i++) dp[i] = Math.min(dp[i-1]+x, dp[(i+1)/2]+y+(i%2)*x);
        out.println(dp[n]);
    }

    public static void main(String[] args)
    {
        in = new FastReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();

    }

    static class FastReader {

        BufferedReader read;
        StringTokenizer tokenizer;

        public FastReader(InputStream in)
        {
            read = new BufferedReader(new InputStreamReader(in));
        }

        public String next()
        {
            while(tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try{
                    tokenizer = new StringTokenizer(read.readLine());
                }catch(Exception e){
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nint()
        {
            return Integer.parseInt(next());
        }
        public long nlong()
        {
            return Long.parseLong(next());
        }
        public double ndouble()
        {
            return Double.parseDouble(next());
        }

        public int[] narr(int n)
        {
            int[] a = new int[n];
            for(int i=0; i<n; ++i)
            {
                a[i] = nint();
            }
            return a;
        }

        public long[] nlarr(int n)
        {
            long[] a = new long[n];
            for(int i=0; i<n; ++i)
            {
                a[i] = nlong();
            }
            return a;
        }
    }


}