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.io.*;


public class ecg
{   




   
   public static void main (String[] args) throws Exception{
    Scanner sc=new Scanner(System.in);
    int a=sc.nextInt();
    int b=sc.nextInt();
    int c=sc.nextInt();
    int n=a*b*c;
    int arr[]=new int[1000005];
    for(int i=1;i<=n;i++){
         for(int j=1;i*j<=n;j++){
          //System.out.println("i: "+i+" j: "+j+" i*j: "+i*j);
                arr[i*j]++;
         }
    }
   // for(int i=1;i<arr.length;i++){
   //  if(arr[i]!=0)
   //  System.out.println(arr[i]+" "+i);
   // }
    int 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];
          sum%=1073741824 ;
        }
      }
    }
    System.out.println(sum);



}

    }