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:
/*
 * Code Author: Akshay Miterani
 * DA-IICT
 */
import java.io.*;

import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
public class MainB {

	static double eps=(double)1e-6;
	static long mod=(int)1e9+7;
	public static void main(String args[]){
		InputReader in = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		//----------My Code----------
		int n=in.nextInt();
		long x=in.nextInt();
		long y=in.nextInt();
		long dp[]=new long[n+1];
		//Arrays.fill(dp, Long.MAX_VALUE);
		dp[0]=0;
		for(int i=1;i<=n;i++){
			dp[i]=Math.min(dp[i-1]+x, dp[(i+1)/2]+y+x*(i%2));
		}
		//debug(dp);
		System.out.println(dp[n]);
		out.close();
		//---------------The End------------------

	}
	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
	static class Pair implements Comparable<Pair>{
		int x;
		int y;
		int i;
		Pair(int xx,int yy){
			x=xx;
			y=yy;
		}
		@Override
		public int compareTo(Pair o) {
			return Integer.compare(this.x, o.x);
		}
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) {
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine(){
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}