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.*;

public class cf236B{

	public static void main(String args[])
	{
	
		Scanner sc =  new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();
		
		int[] bitmap = new int[1000001];
		bitmap[1] = 1;
		for(int i=2; i<=1000000; i++)
			bitmap[i] = 2;
	
		for(int i=2; i<=1000000; i++)
		{
			for(int j=i+i; j<=1000000; j+=i)
			{
							
				bitmap[j] += 1;
				
			}
		
		}
		
		int sum = 0;
		int m = 1;
		m = (m << 30) - 1;
		for(int i=1;i<=a; i++)
			for(int j=1; j<=b; j++)
				for(int k=1; k<=c; k++)
					sum = ((sum + bitmap[i*j*k])&m);		
		
		System.out.println(sum);
	
	}

}