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 EasyNumberChallenge {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long sum = 0;
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        long nr[] = new long[1000001];
        long to = a * b * c;
        for(int i = 1; i <= to; i++) {
            nr[i] = 0;
        }
            nr[1] = 1;
        for(int i = 2; i <= to; i++) {
            for(int j = i; j <= to; j+=i) {
                nr[j]++;
            }
        }
        for(int i = 2; i <= to; i++)
            nr[i]++;
        for(int i = 1; i <= a; i++) {
            for(int j = 1; j <= b; j++) {
                for(int k = 1; k <= c; k++) {
                    sum = sum + nr[i * j * k];
                    if(sum >= 1073741824)
                    {
                        sum = sum % 1073741824;
                    } 
                }
            }
        }
        System.out.println(sum);
    }
}