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.util.Arrays;
import java.util.Scanner;
public class EasyNumberChallenge {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt(), b = sc.nextInt(), c = sc.nextInt(), max = a*b*c, ans = 0, prod;
        int[] NumOfFactors = new int[max + 1];
        Arrays.fill(NumOfFactors, 1);
        for(int i = 2; i <= max; i++) for(int j = i; j <= max; j += i) ++NumOfFactors[j];
        for(int i = 1; i <= a; ++i)
            for(int j = 1; j <= b; ++j) {
                prod = i * j;
                for(int k = 1; k <= c; k++) ans += NumOfFactors[prod * k];
            }
        System.out.println(ans);
        sc.close();
    }
}