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:
// CodeForces Educational Round 16 -- slowe

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class E16 {
	public static void main(String[] args) throws Exception {
		FastScanner in = new FastScanner();
		PrintWriter pw = new PrintWriter(System.out);
		
		int n = in.nextInt(), x = in.nextInt(), y = in.nextInt();
		long[] time = new long[n+1];
		time[1] = x;
		for(int i = 2; i <= n; i++)
			time[i] = Math.min(time[i-1] + x, time[(i+1)/2] + y + (i%2)*x);
		pw.println(time[n]);
		
		pw.flush();
		pw.close();
	}
	
	// if last move was add, subtract is pointless
	// if last move was double, subtraction may be helpful
	// if last move was subtract, previous move must have been double,
	//   so another subtraction yields foo-d-s-s for 2*foo-2
	//   which is equal to 2*(foo-1) from foo-s-d
	//   however, the latter is cheaper, so never subtract twice
	// thus only subtract after doubling
	
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = new StringTokenizer("");
		}
		
		String next() throws Exception {
			while(!st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		
		int nextInt() throws Exception {
			return Integer.parseInt(next());
		}
	}
}