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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		 Scanner sc=new Scanner(System.in);
		 int g=sc.nextInt();
		 int b=sc.nextInt();
		 int c=sc.nextInt();
		 int z=g*b*c; int a[]=new int[z];
// 		 for(int i=0;i<z;i++){
// 		     int k=i+1; a[i]=1;
// 		     for(int j=2;j<=Math.sqrt(k);j++){
// 		         int count=0;
// 		         while(k%j==0){
// 		             k=k/j;count++;
// 		         }
// 		         if(count>0) a[i]*=(count+1);
// 		     }
// 		     if(k>1) a[i]*=2;
// 		 }
         for(int i=1;i<=z;i++){
            for(int j=i;j<=z;j+=i){
                a[j-1]++;
            }
        }
		 long ans=0;
		 for(int i=1;i<=g;i++){
		     for(int j=1;j<=b;j++){
		         for(int k=1;k<=c;k++){
		             ans=(ans+a[(i*j*k)-1])%1073741824;
		         }
		     }
		 }
		 
		 System.out.println(ans);
		 
		 
	   //for(int i=0;i<z;i++){System.out.println(i+1+" "+a[i]);}	 
	}
}