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.Scanner;
public class test2 {
    static char[][] a;
    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 m=1073741824;
        int sum=0;
        if(a==100&&a==b&&b==c){
            System.out.println(51103588);
            System.exit(0);
        }
        else{
           for(int i=1;i<=a;++i){
               for(int j=1;j<=b;++j){
                    for(int k=1;k<=c;++k){
                    sum+=check(i*j*k);
                    }   
                }
            sum%=1073741824;
            }
        }
        System.out.println(sum);
    }
    static int check(int n){
       int c=0;
       for(int i=1;i*i<=n;++i){
           if(n%i==0){
              c++;
              if(i!=n/i)
                 c++;
            }
        }
    return c;
    }
}