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:

<image>

Find the sum modulo 1073741824 (230).

Input

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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.
import java.util.*;
public class MyClass {
    public static void main(String args[]) {
      Scanner sc=new Scanner(System.in);
      int a=sc.nextInt();
      int b=sc.nextInt();
      int c=sc.nextInt();
      int s=0,ans=0;
      int[] arr=new int[1000001];
      for(int i=0;i<1000001;i++)
      arr[i]=0;
      for(int i=1;i<=a;i++)
      {
          for(int j=1;j<=b;j++)
          {
              for(int k=1;k<=c;k++)
              {
                  s=i*j*k;
                  if(arr[s]==0)
                  { int count=0;
                  for(int p=1;p<=Math.sqrt(s);p++)
                  {
                      if(s%p==0)
                      {
                          if(s/p==p)
                          count++;
                          else
                          count=count+2;
                      }
                  }
                  
                  arr[s]=count;
                  ans=ans+count;
                  }
                  
                  else
                  ans=ans+arr[s];
              }
          }
      }
     
    
      System.out.println(ans%1073741824);
    }
}