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:
//package main;
import java.util.*;
import java.math.*;
import java.io.*;
public class Main {
    static StringTokenizer st;
    static BufferedReader scan;
    static PrintWriter out;
    public static void main(String[] args) throws IOException{
        //Scanner sscan = new Scanner(new File("input.txt"));
        //PrintStream oout = new PrintStream(new File("output.txt"));
        scan = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int[] d = new int[1000001];
        for(int i = 1; i <= 1000000; i++){
            for(int j = i; j <= 1000000; j += i)
                d[j]++;
        }
        int a = nextInt(), b = nextInt(), c = nextInt();
        long ans = 0;
        for(int i = 1; i<= a; i++){
            for(int j = 1; j <= b; j++){
                for(int k = 1; k <= c; k++)ans += d[i * j * k];
            }
        }
        out.println(ans);
        scan.close();
        out.close();
        //sscan.locale();
        //oout.close();
    }
    private static BigDecimal nextBigDecimal() throws IOException {
        return(new BigDecimal(next()));
    }
    private static BigInteger nextBigInteger() throws IOException {
        return(new BigInteger(next()));
    }
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static String next() throws IOException {
        while(st == null || !st.hasMoreTokens()){
            st = new StringTokenizer(scan.readLine());
        }
        return st.nextToken();
    }
}