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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class TaskE {

    private static final boolean TEST_CASES = false;

    void solve(int testCaseNo, InputReader in, PrintWriter out) {
        final int n = in.nextInt() + 1;
        final long x = in.nextInt(), y = in.nextInt();
        final long[] ans = new long[n + 2];
        Arrays.fill(ans, Long.MAX_VALUE);
        ans[0] = 0;

        for (int i = 1; i <= n; i++)
            ans[i] = i * x;
        for (int i = 2; i <= n; i+=2) {
            ans[i] = Math.min(ans[i], ans[i / 2] + y);
            ans[i + 1] = Math.min(ans[i + 1], ans[i] + x);
            ans[i - 1] = Math.min(ans[i - 1], ans[i] + x);
        }
        out.println(ans[n - 1]);
    }


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

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

        /**
         * @return null if end of stream
         */
        public String readLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        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());
        }

    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int testCases = TEST_CASES ? in.nextInt() : 1;

        TaskE solver = new TaskE();
        for (int testCase = 0; testCase < testCases; testCase++) {
            solver.solve(testCase, in, out);
        }
        out.flush();
        out.close();
    }
}