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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package generatestring;

import java.io.IOException;
import java.io.InputStream;

/**
 *
 * @author PrudhviRaj
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        InputReader ir = new InputReader();
        int n = ir.readInt();
        long x =ir.readLong(),y = ir.readLong();
        long dp[] = new long[n+1];
        dp[1] = x;
        for(int i=2;i<=n;i++){
            if(i%2==0){
                dp[i] = Math.min(dp[i-1]+x, dp[i/2]+y);
            }
            else{
                dp[i] = Math.min(dp[i-1]+x , dp[(i+1)/2]+y+x);
            }
        }
        System.out.println(dp[n]);
    }
    final static class InputReader {

        byte[] buffer = new byte[8192];
        int offset = 0;
        int bufferSize = 0;
        final InputStream in = System.in;

        public int readInt() throws IOException {
            int number = 0;
            int s = 1;
            if (offset == bufferSize) {
                offset = 0;
                bufferSize = in.read(buffer);
            }
            if (bufferSize == -1) {
                throw new IOException("No new bytes");
            }
            for (; buffer[offset] < 0x30 || buffer[offset] == '-'; ++offset) {
                if (buffer[offset] == '-') {
                    s = -1;
                }
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            for (; offset < bufferSize && buffer[offset] > 0x2f; ++offset) {
                number = (number << 3) + (number << 1) + buffer[offset] - 0x30;
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            ++offset;
            return number * s;
        }

        public int[] readIntArray(int n) throws IOException {
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) {
                ar[i] = readInt();
            }

            return ar;
        }

        public int[] readIntArray1(int n) throws IOException {
            int[] ar = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = readInt();
            }

            return ar;
        }

        public long readLong() throws IOException {
            long res = 0;
            int s = 1;
            if (offset == bufferSize) {
                offset = 0;
                bufferSize = in.read(buffer);
            }
            for (; buffer[offset] < 0x30 || buffer[offset] == '-'; ++offset) {
                if (buffer[offset] == '-') {
                    s = -1;
                }
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            for (; offset < bufferSize && buffer[offset] > 0x2f; ++offset) {
                res = (res << 3) + (res << 1) + buffer[offset] - 0x30;
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            ++offset;
            if (s == -1) {
                res = -res;
            }
            return res;
        }

        public long[] readLongArray(int n) throws IOException {
            long[] ar = new long[n];

            for (int i = 0; i < n; i++) {
                ar[i] = readLong();
            }

            return ar;
        }

        public String read() throws IOException {
            StringBuilder sb = new StringBuilder();
            if (offset == bufferSize) {
                offset = 0;
                bufferSize = in.read(buffer);
            }

            if (bufferSize == -1 || bufferSize == 0) {
                throw new IOException("No new bytes");
            }

            for (;
                    buffer[offset] == ' ' || buffer[offset] == '\t' || buffer[offset]
                    == '\n' || buffer[offset] == '\r'; ++offset) {
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            for (; offset < bufferSize; ++offset) {
                if (buffer[offset] == ' ' || buffer[offset] == '\t'
                        || buffer[offset] == '\n' || buffer[offset] == '\r') {
                    break;
                }
                if (Character.isValidCodePoint(buffer[offset])) {
                    sb.appendCodePoint(buffer[offset]);
                }
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            return sb.toString();
        }

        public String read(int n) throws IOException {
            StringBuilder sb = new StringBuilder(n);
            if (offset == bufferSize) {
                offset = 0;
                bufferSize = in.read(buffer);
            }

            if (bufferSize == -1 || bufferSize == 0) {
                throw new IOException("No new bytes");
            }

            for (;
                    buffer[offset] == ' ' || buffer[offset] == '\t' || buffer[offset]
                    == '\n' || buffer[offset] == '\r'; ++offset) {
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            for (int i = 0; offset < bufferSize && i < n; ++offset) {
                if (buffer[offset] == ' ' || buffer[offset] == '\t'
                        || buffer[offset] == '\n' || buffer[offset] == '\r') {
                    break;
                }
                if (Character.isValidCodePoint(buffer[offset])) {
                    sb.appendCodePoint(buffer[offset]);
                }
                if (offset == bufferSize - 1) {
                    offset = -1;
                    bufferSize = in.read(buffer);
                }
            }
            return sb.toString();
        }
    }
}