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 ≤ 100).

Output

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

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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.
import java.util.*;
import java.lang.*;
public class EasyNumberChallenge
{
    public static void main(String[]args)
    {
        Scanner input=new Scanner(System.in);
        while(input.hasNext())
        {
            int w=0,d[]=new int[1000001];
            for(int z=input.nextInt(),y=input.nextInt(),x=input.nextInt();z>0;z--)
                for(int e=y;e>0;e--)
                    for(int q=x,a=w;q>0;q--,a=w)
                    {
                        int t=q*e*z;
                        if(t==1)
                            w+=1;
                        else if(0!=d[t])
                            w+=d[t];
                        else
                        {
                            for(int c=1,f=t;c<f;f=t/c,c++)
                                if(t%c==0)
                                    if(c*c==t)
                                        w++;
                                    else
                                        w+=2;
                            d[t]=w-a;
                        }
                    }
            System.out.println(w);
        }
    }
}