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 {
    private static Scanner scanner = new Scanner(System.in);
    private static int OO = (int) 1e6 + 9;
    private static int[] dx = {0, 0, 1, -1};
    private static int[] dy = {1, -1, 0, 0};

    public static void main(String[] args) {
        int a = scanner.nextInt(), b = scanner.nextInt(), c = scanner.nextInt(), r = 0;
        int[] d = new int[OO];
        for (int i = 1; i <= 1000000; i++) {
            for (int j = i; j <= 1000000; j += i) {
                d[j]++;
            }
        }
        for (int i = 1; i <= a; i++) {
            for (int j = 1; j <= b; j++) {
                for (int k = 1; k <= c; k++) {
                    r += d[i * j * k];
                }
            }
        }
        System.out.println(r);
    }
}