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 Main1 {

    public static void main(String[] args) {
        
        Scanner in = new Scanner(System.in);
        
        //inputs
        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();
        
        int [] arr = new int [1000001];
            
        for(int i=1 ; i<arr.length ; i++)
            for(int j=i ; j<arr.length ; j+=i)
                arr[j]++;
            
        long sum=0;
        for(int i=1 ; i<=a ; i++)
            for(int j=1 ; j<=b ; j++)
                for(int k=1 ; k<=c ; k++)
                    sum += arr[i*j*k] % 1073741824;
        
       
        System.out.println(sum);
       }
    
    }