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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author ssaxena36 FI/O from @uwi
 */
import java.io.*;
import java.util.*;
public class TesttClass
{
   static ArrayList<Integer>list=new ArrayList<>();
   void solution()
    {
        //TesttClass oj=new TesttClass();
    //   oj.SieveOfEratosthenes(101000);
        // System.out.print(list);
        int n=inpi();
        int x=inpi();
        int y=inpi();
       long dp[]=new long[n+1];
       dp[0]=0;
       dp[1]=x;
       for(int i=2;i<=n;i++)
       {
           if(i%2==0)
           {
               dp[i]=Math.min(dp[i-1]+x, dp[i/2]+y); 
           }
           else
           {
               dp[i]=Math.min(dp[i-1]+x, dp[(i+1)/2]+x+y);  //half and then add duplicate
           }
       }
       out.println(dp[n]);
        /*long sum=sum(arr);
        sum=sum/n;
       // out.println(sum+"-->");
        int x=Collections.binarySearch(arr, sum);
        if(x>=0)
        {
            out.println(sum);
        }
        else
        {
            x=Math.abs(x+1);
         //  out.println(x);
            if(x==0)
            {
                out.println(arr.get(0));
            }
            else
            {
                out.println(arr.get(x));
            }
        }
                */
    }
   public long sum(ArrayList<Long> arr)
   { long s=0;
       for(int i=0;i<arr.size();i++)
       {
           s+=arr.get(i);
       }
       return s;
   }
   public void SieveOfEratosthenes(int n)
{
    boolean prime[]=new boolean[n+1]; 
    Arrays.fill(prime, true);
    for (int p=2; p*p<=n; p++)
    {
        if (prime[p] == true)
        {
            for (int i=p*2; i<=n; i += p)
                prime[i] = false;
        }
    }
    // Print all prime numbers
    for (int p=2; p<=n; p++)
    { if (prime[p])
    {
      //  System.out.print(p+" ");
        list.add(p);
    }
}
   // return list;
}
    
    InputStream obj;
    PrintWriter out;
    String check="";
    public static void main(String[] args)throws IOException{
        new TesttClass().main1();
    }
    void main1()throws IOException{
        out=new PrintWriter(System.out);
        obj=check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
       solution();
        out.flush();
        out.close();
    }
    byte inbuffer[]=new byte[1024];
    int lenbuffer=0,ptrbuffer=0;
    int readByte(){
        if(lenbuffer==-1)
            throw new InputMismatchException();
        if(ptrbuffer>=lenbuffer)
        {
            ptrbuffer=0;
            try {
                lenbuffer=obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if(lenbuffer<=0)
            return -1;
        return inbuffer[ptrbuffer++];
    }
    boolean isSpaceChar(int c)
    {
        return (!(c>=33 && c<=126));
    }
    int skip()
    {
        int b;
        while((b=readByte())!=-1 && isSpaceChar(b));
        return b;
    }
    String inps()
    {
        int b=skip();
        StringBuilder sb=new StringBuilder();
        while(!(isSpaceChar(b)))
        {
            sb.appendCodePoint(b);
            b=readByte();
        }
        return sb.toString();
    }
    int inpi()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-')
        {
            minus = true;
            b = readByte();
        }
        while(true)
        {
            if(b >= '0' && b <= '9')
            {
                num = num * 10 + (b - '0');
            }
            else
            {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    long inpl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-')
        {
            minus = true;
            b = readByte();
        }
        while(true)
        {
            if(b >= '0' && b <= '9')
            {
                num = num * 10 + (b - '0');
            }
            else
            {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    float inpf()
    {
        return Float.parseFloat(inps());
    }
    double inpd()
    {
        return Double.parseDouble(inps());
    }
    char inpc()
    {
        return (char)skip();
    }
    int[] inpia(int n)
    {
        int a[]=new int[n];
        for(int i=0;i<n;i++)
            a[i]=inpi();
        return a;
    }
    long[] inpla(int n)
    {
        long a[]=new long[n];
        for(int i=0;i<n;i++)
            a[i]=inpl();
        return a;
    }
    String[] inpsa(int n)
    {
        String a[]=new String[n];
        for(int i=0;i<n;i++)
            a[i]=inps();
        return a;
    }
    double[][] inpdm(int n, int m)
    {
        double a[][]=new double[n][m];
        for(int i=0;i<n;i++)
            for(int j=0;j<m;j++)
                a[i][j]=inpd();
        return a;
    }
    int[][] inpim(int n, int m)
    {
        int a[][]=new int[n][m];
        for(int i=0;i<n;i++)
            for(int j=0;j<m;j++)
                a[i][j]=inpi();
        return a;
    }
}