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.HashMap;
import java.util.Scanner;

public class Main {
    static HashMap<Integer, Integer> divisors = new HashMap<>();
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();

        long answer = 0;
        for(int i = 1; i <= a; i++)
            for(int j = 1; j <= b; j++)
                for(int k = 1; k <= c; k++)
                    answer += calculateDivisors(i * j * k);

        System.out.println(answer % 1073741824);

    }

    private static int calculateDivisors(int n) {
        if(divisors.containsKey(n))
            return divisors.get(n);
        int numberOfDivisors = 0;
        int i;
        for(i = 1; i * i < n; i++) {
            if(n % i == 0)
                numberOfDivisors += 2;
        }
        if(i * i == n)
            numberOfDivisors++;

        divisors.put(n, numberOfDivisors);
        return numberOfDivisors;
    }
}