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 scanner = new Scanner(System.in);
        int a = scanner.nextInt();
        int b = scanner.nextInt();
        int c = scanner.nextInt();

        int arr[] = new int[a*b*c+3];
        for (int i=0;i<arr.length;i++){
            arr[i]=0;
        }

        int result = 0;
        for(int i=1;i<=a;i++){
            for (int j=1; j<=b;j++){
                for (int z = 1 ; z<=c;z++){
                    int x = i*j*z;
                    if(arr[x]==0){
                        arr[x] = numMod(x);
                    }
                    result+=arr[x];
                }
            }
        }
        System.out.println(result%(int)Math.pow(2,30));
    }
    static int numMod(int x){
        int t=0;
        for (int i=1;i*i<=x;i++){
            if(x%i==0){
                t+=2;
            }
        }
        if ((int)Math.sqrt(x)==Math.sqrt(x)){
            t--;
        }
        return t;
    }
}