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.Scanner;

public class NumberChallenge236B {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int a=s.nextInt();
		int b=s.nextInt();
		int c=s.nextInt();
		int MAX = 1000001; // 100*100*100
		int[] d = new int[MAX];
		for (int i=1; i<MAX; i++) {
			for (int j=i; j<MAX; j+=i) {
				d[j]++; // builds divisor function
			}
		}
		long sum=0;
		for (int i=1; i<=a; i++) {
			for (int j=1; j<=b; j++) {
				for (int k=1; k<=c; k++) {
					sum = (sum + d[i*j*k])%1073741824;
				}
			}
		}
		System.out.println(sum);
	}
}
