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:

<image>

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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Hashtable;
import java.util.StringTokenizer;

public class EasyNumberChallenge {
    public static void main(String [] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer strTok = new StringTokenizer(br.readLine());
        int a = Integer.parseInt(strTok.nextToken());
        int b = Integer.parseInt(strTok.nextToken());
        int c = Integer.parseInt(strTok.nextToken());
        long sum = 0;
        Hashtable<Integer, Long> div = new Hashtable<Integer, Long>();
        for(int i=1; i<=a; i++) {
            for(int j=1; j<=b; j++) {
                for(int k=1; k<=c; k++) {
                    long d = 0;
                    int product = i*j*k;
                    if(div.containsKey(product)) {
                        d = div.get(product);
                    } else {
                        d = divisors(product);
                        div.put(product, d);
                    }
                    sum += d;
                }
            }
        }
        System.out.println((sum % 1073741824));
    }

    private static long divisors(int x) {
        if(x == 1) {
            return 1;
        }
        int count = 2;
        int sqrt = (int) Math.sqrt(x);
        for(int i=2; i<=sqrt; i++) {
            if(x%i == 0) {
                count+=2;
            }
        }
        if(sqrt*sqrt == x) {
            count -= 1;
        }
        return count;
    }
}
