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{
  static int arr[]=new int[1000001];
  public static int div(int a){
    if(arr[a]!=0){
      return arr[a];
    }
    int count=0;
    for(int i=1;i*i<=a;i++){
      if(a%i==0){
        count++;
        if(i*i!=a){
          count++;
        }
      }
      
    }
    arr[a]=count;
      return arr[a];
  }
  public static void main(String args[]){
    Scanner sc=new Scanner(System.in);
    
    int a,b,c;
    a=sc.nextInt();
    b=sc.nextInt();
    c=sc.nextInt();
    int ans=0;
    for(int i=1;i<=a;i++){
      for(int j=1;j<=b;j++){
        for(int k=1;k<=c;k++){
          ans+=div(i*j*k);
        }
      }
    }
    System.out.println(ans);
  }
}