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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		PrintWriter out=new PrintWriter(System.out);
		int dp[]=new int[(100*100*100)+1];
		for(int i=1;i<1000001;i++) {
		    for(int j=i;j<1000001;j=j+i) {
		        ++dp[j];
		    }
		}
		Scanner sc=new Scanner(System.in);
		int a=sc.nextInt();
		int b=sc.nextInt();
		int c=sc.nextInt();
		long res=0l;
		for(int i=1;i<=a;i++) {
		    for(int j=1;j<=b;j++) {
		        for(int k=1;k<=c;k++) {
		            res+=dp[i*j*k];
		        }
		    }
		}
		res%=1000000007;
		out.println(res);
			out.flush();
	out.close();
	}

}