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.*;

public class EasyNumber
{  
	public static void main(String[]args)
	{
		Scanner in=new Scanner(System.in);
		int a=in.nextInt();
		int b=in.nextInt();
		int c=in.nextInt();
		int i,j,k,sum=0;;
      int[]arr=new int[1000001];
      for( i=1;i<=1000000;i++)
      	for(j=i;j<=1000000;j=j+i)
      		arr[j]++;
		for(i=1;i<=a;i++)
      {
    	  for(j=1;j<=b;j++)
    	  {
    		  for(k=1;k<=c;k++)
    		  {
    			 sum+=arr[i*j*k]; 
    		  }
    	  }
      }
      System.out.println(sum);
    }
    
}