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 NumChallenge {
        public static void main(String[] args) {
                Scanner in = new Scanner(System.in);
                
int a,b,c,i,j,divisors=0;
a = in.nextInt();
b = in.nextInt();
c = in.nextInt();
 int[]arr=new int[1000001];
      for( i=1;i<=1000000;i++){
      	for(j=i;j<=1000000;j+=i){
      		arr[j]++;}}
      
            for ( i = 1; i <= a; i++) {
                for ( j = 1; j <= b; j++) {
                    for (int k = 1; k <= c; k++) {
                        int div=i*j*k;
                         divisors += arr[div];
                    }
                }
            }
           System.out.println(divisors);
        
        }
}