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 easynumberchallenge {
	
	static int divisores(int a, int b, int c, int[] arreglo){
		int suma = 0;
		for(int i=1;i<(a*b*c)+1;i++){
			for(int j=1;j<=(a*b*c)/i;j++){
				arreglo[i*j]=arreglo[i*j]+1;
			}
		}
		for(int k=1;k<=a;k++){
			for(int l =1;l<=b;l++){
				for(int m=1;m<=c;m++){
					suma=suma+arreglo[k*l*m];
				}
			}
		}
		return suma;
	}
	
	public static void main(String[] args){
		
		Scanner S = new Scanner(System.in);
		
		int a = S.nextInt();
		
		int b = S.nextInt();
		
		int c = S.nextInt();
		
		int[] arreglo = new int[a*b*c+1];
		
		int sumita= divisores(a,b,c,arreglo);
		
		System.out.println(sumita);
	}

}