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.ArrayList;
import java.util.HashMap;


public class Main {

    public static void main(String[] args)throws IOException {
		BufferedReader br  = new BufferedReader(new InputStreamReader(System.in));
		OutputStream out = new BufferedOutputStream(System.out);
        HashMap<Long,Long> map  = new HashMap<>();
	    String[] ss = br.readLine().split(" ");
	    int a = Integer.parseInt(ss[0]);
	    int b = Integer.parseInt(ss[1]);
	    int c = Integer.parseInt(ss[2]);
	    long ans =0;
	    long sum =0;
	    long count=0;
	    for(int i=1;i<=a;i++){
	        for(int j=1;j<=b;j++){
	            for(int k =1;k<=c;k++){
	                ans = i*j*k;
	                if(!map.containsKey(ans)) {
                        if (ans == 1) {
                            count = 1;
                        }
                        else {
                            count = 0;
                            for (int h = 1; h <= Math.sqrt(ans); h++) {
                                if (ans % h == 0 && ans / h != h) {
                                    count += 2;
                                } else if (ans % h == 0 && ans / h == h) {
                                    count++;
                                }
                            }
                        }
                        map.put(ans,count);
                        sum += count;
                    }
	                else{
	                    sum +=map.get(ans);
                    }
	                sum =sum %1073741824;
                }
            }
        }
	    long hh = sum % 1073741824;
	    String uu = "";
	    uu +=hh;
        out.write((uu + "\n").getBytes());
        out.flush();
    }
}
