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.Scanner;

public class Main {

    public static void main(String[] args) {
        int sum = 0;
        Scanner scanner=new Scanner(System.in);
        int x=scanner.nextInt();
        int y=scanner.nextInt();
        int z=scanner.nextInt();
        for (int i =1;i<x+1;i++) {
            for (int j = 1; j < y + 1; j++) {
                for (int k = 1; k < z + 1; k++) {
                    sum = sum + d(i * j * k);
                }
            }
        }
        System.out.print(sum);

    }

    private static int d(int x) {
        int i = 2;
        int div = 1;
        int t = 0;
        while(x>1){
            if(x%i == 0){
                x/=i;
                t+=1;
            }
            else{
                i+=1;
                div*=(t+1);
                t=0;
            }
            
        }
        div*=(t+1);
        return div;
    }
}