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.*;
import java.lang.*;
public class R
{  
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in); int a = sc.nextInt(), b = sc.nextInt(), c = sc.nextInt();
        long ans = 0;
        int[][] arr = new int[b+1][c+1];
        int[] divisor=new int[10000000];
        int n=a*b*c;
        for(int i=1;i<=n;i++) {
            for(int j=i;j<=n;j+=i) {
                divisor[j]++;
            }
        }
            //System.out.println(Arrays.toString(divisor));
        for(int j = 1; j<=b; j++) {
                for(int z = 1; z<=c; z++) {
                     arr[j][z] = j*z;
                }
            }
        for(int i = 1; i<=a; i++) {
            for(int j = 1; j<=b; j++) {
                for(int z = 1; z<=c; z++) {
                    ans += divisor[i*arr[j][z]];
                }
            }
        }
        System.out.println(ans); 
    }
 
}