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;

/**
 *
 * @author dilshan
 */
public class Facotor {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner s = new Scanner(System.in);
        int a = s.nextInt();
        int b = s.nextInt();
        int c = s.nextInt();
        int max = a * b * c;
        int sum = 0;
        int[] m = new int[max + 1];
        int d = 0;
        for (int i = 1; i <= a; ++i) {
            for (int j = 1; j <= b; ++j) {
                for (int k = 1; k <= c; ++k) {
                    d = i * j * k;
                    if (m[d] > 0) {
                        sum += m[d];
                    } else {
                        m[d] = Facotor.find(i, j, k);
                        sum += m[d];
                    }
                }
            }
        }
        System.out.println(sum);

    }

    static int find(int a, int b, int c) {
        int mul = a * b * c;
        int count = 0;
        for (int i = 1; i <= Math.sqrt(mul);++i) {
            if (mul % i == 0) {
                ++count;
                
                if(i!=Math.sqrt(mul)){
                    ++count;
                }
            }
        }
        return count ;
    }
}