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.io.FileNotFoundException;
import java.util.*;

public class _236B_Easy_Number_Challenge {
    public static void main(String[] args) throws FileNotFoundException {
	Scanner in = new Scanner(System.in);
	int a = in.nextInt();
	int b = in.nextInt();
	int c = in.nextInt();

	int MAX = 1000001;
	int d[] = new int[MAX];

	for (int i = 1; i < MAX; i++)
	    for (int j = i; j < MAX; j += i)
		d[j]++;

	long r = 0;
	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 % 1073741824);
    }
}