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.*;
import java.util.*;
import java.math.*;

public class B236 {

	public static BufferedReader read = null;
	public static PrintWriter out = null;
	public static StringTokenizer token = null;
	
	
	public static void solve()
	{
		long mod = 1l << 30;
		int max = 100*100*100;
		int d[] = new int[max+1];
		for(int i=1; i<=max; i++ )
		{
			for(int j = i; j<=max; j+=i)
			{
				d[j]++;
			}
		}
		int a = nint();
		int b = nint();
		int c = nint();
		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+=d[i*j*k]%mod;
				}
		out.println(sum%mod);
		
	}
	
	public static void main(String[] args)
	{
		read = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		out.close();
		
	}
	
	// i/o functions
	public static String next() // returns the next string
	{
		while(token == null || !token.hasMoreTokens())
		{
			try {
				token = new StringTokenizer(read.readLine());
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
		return token.nextToken();
	}
	
	public static int nint()
	{
		return Integer.parseInt(next());
	}
	public static long nlong()
	{
		return Long.parseLong(next());
	}
	public static double ndouble()
	{
		return Double.parseDouble(next());
	}
	public static int[] narr(int n)
	{
		int[] a = new int[n];
		for(int i=0; i<n; i++) a[i] = nint();
		return a;
	}
	
	public static long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i=0; i<n; i++) a[i] = nlong();
		return a;
	}
	
	
}