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 input = new Scanner(System.in);

        int x = input.nextInt();
        int y = input.nextInt();
        int z = input.nextInt();
        int sum = 0;
        int[] g = new int[1000001];
        for (int i = 1; i <= x; i++) {
            for (int j = 1; j <= y; j++) {
                for (int k = 1; k <= z; k++) {
                    if (g[(i * j * k)] > 0) {
                        sum += g[(i * j * k)];
                    } else {
                        g[(i * j * k)] = div((i * j * k));
                        sum += g[(i * j * k)];

                    }
                }
            }
        }
        System.out.println(sum);
    }

    public static int div(int t) {
        int l = 0;

        if (t == 1) {
            return 1;
        } else {
            for (int i = 1; i * i <= t; i++) {
                if (t % i == 0 && t / i != t / (t / i)) {
                    l += 2;
                } else if (t % i == 0 && t / i == t / (t / i)) {
                    l += 1;
                }
            }
            return l;
        }

    }
}