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.*;
public class MyClass {
    public static void main(String args[]) {
        Scanner sc=new Scanner(System.in);
        int a=sc.nextInt(),b=sc.nextInt(),c=sc.nextInt();
        long[] div=new long[1000001];
        Arrays.fill(div,1);
        div[0]=0;
        div[1]=1;
        for(int i=2;i<1000001;i++){
            for(int j=i;j<1000001;j+=i)
                div[j]++;
        }
        
        long sum=0,m=1073741824;
        for(int i=1;i<=a;i++)
            for(int j=1;j<=b;j++)
                for(int k=1;k<=c;k++){
                    sum=((sum%m)+(div[i*j*k])%m)%m;
                }
        
        System.out.println(sum);
    }
}
