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:

<image>

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.*;

public class easyNumber {
    static int [] solution = new int[1000001];
    public static int d(int a){
        if(solution[a] != 0){
            return solution[a];
        }
        int ans = 0;
        for (int i = 1; i * i <= a ; i++) {
            if(a % i == 0){
                ans++;
                if(i * i != a){
                    ans++;
                }
            }
        }
        solution[a] = ans;
        return ans;
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int a = in.nextInt(),b = in.nextInt(),c = in.nextInt(),ans = 0;
        for (int i = 1; i <= a ; i++) {
            for (int j = 1; j <= b; j++) {
                for (int k = 1; k <= c ; k++) {
                    ans+=d(i*j*k);
                }
            }
        }
        System.out.println(ans%1073741824);
    }
}