Problem: Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:

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Find the sum modulo 1073741824 (230).

Input

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 2000).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

4 4 4


Output

328


Input

10 10 10


Output

11536

Note

For the first example.

  * d(1·1·1) = d(1) = 1; 
  * d(1·1·2) = d(2) = 2; 
  * d(1·2·1) = d(2) = 2; 
  * d(1·2·2) = d(4) = 3; 
  * d(2·1·1) = d(2) = 2; 
  * d(2·1·2) = d(4) = 3; 
  * d(2·2·1) = d(4) = 3; 
  * d(2·2·2) = d(8) = 4. 



So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
/**
 * @author Alvex - GoldenReam1503@gmail.com
 * Time: 12:41:28 PM
 * Date: Nov 14, 2015
 */
public class _236B_Easy_Number_Challenge
{
    private static class Output
    {
        private final PrintWriter printer;
        public void printLine(Object...objects) 
        {
            print(objects);
            printer.println();
        }
        public void print(Object...objects) 
        {
            int i;
            for (i=0;i<objects.length;i++) 
            {
                if (i!=0)
                    printer.print(' ');
                printer.print(objects[i]);
            }
        }
        public Output(OutputStream outputStream)
        {
            printer= new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        public void flush()
        {
            printer.flush();
        }
        public void close()
        {
            printer.close();
        }
    }
    private static class Input
    {
        private InputStream stream;
        private byte Buffer[]=new byte[1024];
        private int curChar;
        private int numberChars;
        private SpaceCharFilter filter;
        public interface SpaceCharFilter 
        {
            public boolean isSpaceChar(int ch);
        }
        public Input(InputStream stream)
        {
            this.stream=stream;
        }
        public static boolean isWhitespace(int c) 
        {
            boolean flag=false;
            if(c==' '|| c=='\n' || c=='\r' || c=='\t' || c==-1)
                flag=true;
            return flag;
        }
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }
        public int read()
        {
            if (numberChars==-1)
                throw new InputMismatchException();
            if (curChar>=numberChars) 
            {
                curChar = 0;
                try 
                {
                    numberChars = stream.read(Buffer);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (numberChars <= 0)
                    return -1;
            }
            return Buffer[curChar++];
        }
        public int readInt() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } 
            while (!isSpaceChar(c));
            return res * sgn;
        }
    }
    public static final int modulo=1073741824;
    public static int divisor[]=new int[10000000];
    public static void main(String[] args)
    {   
        Input in=new Input(System.in);
        Output out=new Output(System.out);
        int a=in.readInt(), b=in.readInt(), c=in.readInt();
        int i,j,k;
        int n=a*b*c;
        for(i=1;i<=n;i++)
            for(j=i;j<=n;j+=i)
                divisor[j]++;
        long ans=0;
        for(i=1;i<=a;i++)
            for(j=1;j<=b;j++)
                for(k=1;k<=c;k++)
                    ans+=divisor[i*j*k]%modulo;
        out.printLine(ans);
        out.flush();
        out.close();
    }
}