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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class E {

    public static void main(String args[]) {
        E e = new E();
        e.solve(System.in, System.out);
    }

    public void solve(InputStream in, OutputStream out) {
        InputReader inputReader = new InputReader(in);
        PrintWriter writer = new PrintWriter(new BufferedOutputStream(out));

        int n = inputReader.nextInt();
        long x = inputReader.nextLong();
        long y = inputReader.nextLong();

        writer.write(solve(n, x, y) + "\n");
        writer.close();
    }

    public long solve(int n, long x, long y) {
        long d[] = new long[n + 1];
        d[0] = 0;
        for (int i = 1; i <= n; i++) {
            d[i] = Long.MAX_VALUE;
        }

        for (int i = 1; i <= n; i++) {
            d[i] = Math.min(d[i], d[i - 1] + x);
            if (i % 2 == 0) {
                d[i] = Math.min(d[i], d[i / 2] + y);
            } else {
                d[i] = Math.min(d[i], d[(i + 1) / 2] + x + y);
            }
        }

        return d[n];
    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        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 int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}