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 com.sun.org.apache.bcel.internal.generic.FieldGen;

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    class GraphBuilder {
        int n, m;
        int[] x, y;
        int index;
        int[] size;


        GraphBuilder(int n, int m) {
            this.n = n;
            this.m = m;
            x = new int[m];
            y = new int[m];
            size = new int[n];
        }

        void add(int u, int v) {
            x[index] = u;
            y[index] = v;
            size[u]++;
            size[v]++;
            index++;
        }

        int[][] build() {
            int[][] graph = new int[n][];
            for (int i = 0; i < n; i++) {
                graph[i] = new int[size[i]];
            }
            for (int i = index - 1; i >= 0; i--) {
                int u = x[i];
                int v = y[i];
                graph[u][--size[u]] = v;
                graph[v][--size[v]] = u;
            }
            return graph;
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long[] readLongArray(int size) throws IOException {
        long[] res = new long[size];
        for (int i = 0; i < size; i++) {
            res[i] = readLong();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Template().run();
        // new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    void solve() throws IOException {
        int n = readInt();
        int x = readInt();
        int y = readInt();
        long[] dp = new long[n + 1];
        for (int i=1;i<=n;i++) {
            dp[i] = dp[i - 1] + x;
            if (i % 2 == 0) {
                dp[i] = Math.min(dp[i], dp[i / 2] + y);
            } else {
                dp[i] = Math.min(dp[i], Math.min(dp[(i / 2) + 1], dp[i / 2]) + x + y);
            }
        }
        out.println(dp[n]);
    }

}