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 sc = new Scanner(System.in);
        int i=sc.nextInt(),j=sc.nextInt(),k=sc.nextInt();
        int sum=0;
        int arr[]= new int[1000001];
        for(int x=1;x<=i;x++){
            for(int y=1;y<=j;y++){
                for(int z=1;z<=k;z++){
                    if(arr[x*y*z]!=0) sum+=arr[x*y*z];
                    else {arr[x*y*z]=noDiv(x*y*z);
                    sum+=arr[x*y*z];}
                }
            }
        }
        System.out.println(sum);
    }
    static int noDiv(int n) { 
    int no=0;
        for (int i=1; i<=Math.sqrt(n); i++)      
            if (n%i==0) 
                if (n/i == i) no++;
                else no+=2;             
        return no;
    }}