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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class EZNumChallenge {

	public static void main (String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] input = br.readLine().split(" ");
		int a = Integer.parseInt(input[0]);
		int b = Integer.parseInt(input[1]);
		int c = Integer.parseInt(input[2]);
		
		int[] criba = new int[a*b*c+1];
		for (int i = 1; i <= a*b*c; i++){
			for (int j = 1; i*j <= a*b*c; j++){
				criba[i*j]++;
			}
		}
		
		long count = 0;
		for (int i = 1; i <= a; i++){
			for (int j = 1; j <= b; j++){
				for (int k = 1; k <= c; k++){
					count = (count + criba[i*j*k])%1073741824;
				}
			}
		}
		System.out.println(count);
	}
}