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.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import static java.lang.System.*;
import java.math.BigInteger;
import java.util.List;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;

public class cf236b_eac {

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static Scanner sc = new Scanner(System.in);

    public static String getString() {
        try {
            return br.readLine();
        } catch (Exception e) {
        }
        return "";
    }

    public static Integer getInt() {
        try {
            return Integer.parseInt(br.readLine());
        } catch (Exception e) {
        }
        return 0;
    }

    public static Integer[] getIntArr() {
        try {
            String temp[] = br.readLine().split(" ");
            Integer temp2[] = new Integer[temp.length];
            for (int i = 0; i < temp.length; i++) {
                temp2[i] = Integer.parseInt(temp[i]);
            }
            return temp2;
        } catch (Exception e) {
        }
        return null;
    }

    public static int getMax(Integer[] ar) {
        int t = ar[0];
        for (int i = 0; i < ar.length; i++) {
            if (ar[i] > t) {
                t = ar[i];
            }
        }
        return t;
    }

    public static void printList(List<Integer> a) {
        System.out.println(a.toString().replace("[", "").replace("]", "").replace(",", ""));
    }

    public static void print(Object a) {
        out.println(a);
    }

    public static int nextInt() {
        return sc.nextInt();
    }

    public static double nextDouble() {
        return sc.nextDouble();
    }

    public static BigInteger getFact(long in) {
        BigInteger ot = new BigInteger("1");
        for (Integer i = 1; i <= in; i++) {
            ot = ot.multiply(new BigInteger(i.toString()));
        }
        return ot;
    }

    public static String gbase(int a, int base) {
        String out = "";
        int temp = a;
        while (temp > 0) {
            out = temp % base + out;
            temp /= base;
        }
        return out;
    }

    public static long sol(long m) {
        if (m == 1) {
            return 1;
        }
        long m2 = m;
        if(map.containsKey(m)){
            return map.get(m);
        }
        long out = 1;
        for (long i = 2; i <= m; i++) {
            long ct = 1;
            while (m % i == 0) {
                //print(i + " " + m);
                ct++;
                m /= i;
            }
            out *= ct;
        }
        map.put(m2, out);
        //print(out);
        return out;
    }

    public static long sol2(long m) {
        if (m == 1) {
            return 1;
        }
        long out = 1;
        for (long i = 2; i <= m; i++) {
            if (m % i == 0) {
                print(i);
                out++;
            }
        }
        //print(out);
        return out;
    }
    static HashMap<Long, Long> map = new HashMap<Long, Long>();

    public static void main(String[] ar) {

        int a = nextInt();
        int b = nextInt();
        int c = nextInt();
        //prima(a * b * c);
        long tot = 0;
        for (int i = 1; i <= a; i++) {
            for (int j = 1; j <= b; j++) {
                for (int k = 1; k <= c; k++) {
                    long temp = i * j * k;
                    //print(i+"*"+j+"*"+k+"="+temp + " "+sol(temp));
                    tot += sol(temp);
                }
            }
        }
        print(tot % 1073741824);

    }
}