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:

<image>

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.*;
import java.math.BigInteger;
import java.util.*;
public class Temp3 {
	public static void main(String[] args) throws Throwable {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		long[] arr = new long[1000001];
		for (int i = 1; i < arr.length; i++)
		{
			for (int j = i; j < arr.length; j+=i) 
			{
				arr[j]++;
			}
		}
		long ans = 0;
		int a = Integer.parseInt(st.nextToken());
		int b = Integer.parseInt(st.nextToken());
		int c = Integer.parseInt(st.nextToken());
		for (int i = 1; i <= a; i++) 
		{
			for (int j = 1; j <=b; j++) 
			{
				for (int k = 1; k <= c; k++) 
				{
					int cur = i*j*k;
					ans+=arr[cur];
				}
			}
		}
		System.out.println(ans);
	}
}