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.HashMap;
import java.util.Scanner;
 
public class Section {
    private static HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        int sum = 0;
        for (int i = 1; i <= a; i++) {
            for (int j = 1; j <= b; j++) {
                for (int k = 1; k <= c; k++) {
                    sum +=count(i*j*k);
                }
            }
        }
        System.out.println(sum%1073741824);
    }
 
    private static int count(int j){
        int count =0;
        if(map.containsKey(j)){
            return map.get(j);
        }
        for (int i = 1; i <= Math.sqrt(j); i++)
        {
            if (j % i == 0) {
                // If divisors are equal,
                // count only one
                // because it will be once number can be divisored by
                if (j / i == i)
                    count++;
 
                else // Otherwise count both
                    // ,cause it will be the number and one of it is doubles
                    count += 2;
            }
        }
        map.put(j, count);
        return count;
    }
 
}