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.*;
import java.io.*;

public class Main {


    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter/*(new File("Omar.txt"));*/(System.out);


String[] parts=br.readLine().split(" ");
        int a=Integer.parseInt(parts[0]);
        int b=Integer.parseInt(parts[1]);
        int c=Integer.parseInt(parts[2]);
        int[]d=new int[1000001];
        int i,j;
        for( i=1;i<=1000000;i++)
            for(j=i;j<=1000000;j=j+i)
                d[j]++;
        long answer=0;
        int k;
        for(i=1;i<=a;i++){
            for(j=1;j<=b;j++){
                for(k=1;k<=c;k++){
                    answer+=d[i*j*k];
                   // System.out.println(i*j*k);
                    answer=answer%1073741824L;

                }
            }
        }
pw.print(answer);
pw.print('\n');
       // System.out.println(Arrays.toString(a));
//        counter+=Math.min(less,greater);

        br.close();
        pw.close();
    }
}