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 ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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

public class Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        String s[]=bu.readLine().split(" ");
        int a=Integer.parseInt(s[0]),b=Integer.parseInt(s[1]),c=Integer.parseInt(s[2]);
        int i,j,k,ans=0,M=1073741824;
        HashMap<Integer,Integer> hm=new HashMap<>();
        for(i=1;i<=a;i++)
        for(j=1;j<=b;j++)
        for(k=1;k<=c;k++)
        {
            int p=i*j*k;
            if(hm.get(p)==null) hm.put(p,countdiv(i*j*k));
            ans=(ans+hm.get(p))%M;
        }
        System.out.print(ans);
    }

    static int countdiv(int n)
    {
        int i,c=0;
        for(i=1;i*i<=n;i++)
        if(n%i==0)
        {
            if(n/i==i) c--;
            c+=2;
        }
        return c;
    }
}