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:

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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 ≤ 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.Scanner;

public class EasyNumberChallenge {
    static int d[] = new int[10000001];
    static long d(int a){
        int count = 0;
        for(int i = a;i>=1;i--){
            count = a%i==0?count+1:count;
        }
        return count;
    }
    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 res = 0;
        int t=a*b*c;
        for(int i=1;i<=t;++i)
            for(int j=1;j*i<=t;++j) d[i*j]++;
        for(int i=1;i<=a;++i)
            for(int j=1;j<=b;++j)
                for(int k=1;k<=c;++k) res=(res+d[i*j*k]);

        System.out.println(res%1073741824);
    }
}