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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class _408B {

    /**
     * @param args
     * @throws IOException 
     */
    public static void main(String[] args) throws IOException {
        BufferedReader r=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer n=new StringTokenizer(r.readLine());
                
    //  boolean arr[] = new boolean[10];
    //Arrays.fill(arr, false);  
int a=Integer.parseInt(n.nextToken()),b=Integer.parseInt(n.nextToken()),c=Integer.parseInt(n.nextToken());
int factor[]=new int[1000001];

Arrays.fill(factor,1);
factor[1]=1;

for(int i=2;i<=1000000;i++)
{
    for(int j=1;j<=1000000/i;j++)
    {
        factor[j*i]++;
        
    }
    
    
}

long mod=1<<30;

long result=0;
        for(int i=1;i<=a;i++)
        {
            for(int j=1;j<=b;j++)
            {
                for(int k=1;k<=c;k++)
                {
                    
                    int ds=i*j*k;
            result=result+factor[ds];
            
                    
                }
            
            }
            
        }
        
        result=result%mod;
        
        System.out.println(result);
            

}}