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 {

	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int a=scan.nextInt();
		int b=scan.nextInt();
		int c=scan.nextInt();
		int n=a*b*c;
		int ans[]=new int[1000005];
		for(int i=1;i<=n;i++) {
			for(int j=1;i*j<=n;j++) {
				ans[i*j]++;
			}
		}
		int sum=0;
		for(int i=1;i<=a;i++) {
			for(int j=1;j<=b;j++) {
				for(int k=1;k<=c;k++) {
					sum+=ans[i*j*k];
					sum%=1073741824;
				}
			}
		}
		System.out.println(sum);
	}

}