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:
/*
ID: Aegis
LANG: JAVA
TASK: ProblemB
*/

import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
import java.awt.*;
import java.awt.geom.*;

public class ProblemB {

    static BufferedReader in;
    static PrintStream out;
    static StringTokenizer tok;
    static Scanner sc;
    static PrintWriter writer;

    public static void main(String[] args) throws NumberFormatException, IOException
    {
        in = new BufferedReader(new InputStreamReader(System.in));
        //in = new BufferedReader(new FileReader("in.txt"));
        //in = new BufferedReader(new FileReader("ProblemB.in"));
        //writer = new PrintWriter(new BufferedWriter(new FileWriter("ProblemB.out")));
        out = System.out;
        run();
        //writer.close();
        //System.exit(0);
    }

    static int[] div;
    static boolean[] mask;
    static int count;
    static int mod;

    static void sieve()
    {
        int n = 1000000;
    div = new int[1000001];
        Arrays.fill(div, 1);
        for(int i = 2; i <= n; i++)
            for(int j = i; j <= n; j+= i)
                div[j]++;
    }

    static void run() throws NumberFormatException, IOException
    {
        mod = 1 << 30;
        sieve();
        int a = nextInt();
        int b = nextInt();
        int c = nextInt();
        int res = 0;
        for(int i = 1; i <= a; i++)
            for(int j = 1; j <= b; j++)
                for(int k = 1; k <= c; k++)
                    res = (res + div[i * j * k]) % mod;
        out.println(res);
    }

    static String nextToken() throws IOException
    {
        String line = "";
        if(tok == null || !tok.hasMoreTokens())
        {
            if((line = in.readLine()) != null && !line.equals(""))
                tok = new StringTokenizer(line);
            else
                return null;
        }
        return tok.nextToken();
    }

    static int nextInt() throws NumberFormatException, IOException
    {
        return Integer.parseInt(nextToken());
    }

    static long nextLong() throws NumberFormatException, IOException
    {
        return Long.parseLong(nextToken());
    }

    static double nextDouble() throws NumberFormatException, IOException
    {
        return Double.parseDouble(nextToken());
    }

}