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 Main {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);

        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();

        long m = 1073741824;
        long sum = 0;

        for (int i=1;i<=a;i++) {
            for (int j=1;j<=b;j++) {
                for (int k=1;k<=c;k++) {
                    sum = (sum+d(i*j*k))%m;
                }
            }
        }
        System.out.println(sum);
    }
    public static long d(long x) {
        long res = 1,counter,i = 2;
        while (i*i<=x) {
            counter = 0;
            while (x%i==0) {
                counter++;
                x/=i;
            }
            i++;
            res*=(counter+1);
        }
        if (x>1) {
            res*=2;
        }
        return res;
    }
}