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.*;
public class B {
	Scanner sc = new Scanner(System.in);
	void doIt()
	{
		final int MOD = 1073741824;
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();
		int m = a * b * c;
		int [] cnt = new int[m+1];
		for(int i = 1; i <= m; i++) {
			for(int j = 1; i * j <= m; j++){
				cnt[i*j] ++;
			}
		}
		//System.out.println(Arrays.toString(cnt));
		int ans = 0;
		for(int i = 1; i <= a; i++) {
			for(int j = 1; j <= b; j++) {
				for(int k = 1; k <= c; k++) {
					ans += cnt[i*j*k];
					ans = ans % MOD;
				}
			}
		}
		System.out.println(ans);
	}
	public static void main(String[] args) {
		new B().doIt();

	}

}