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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class B {

    static BufferedReader in;
    static StringTokenizer st;
    static PrintWriter out;

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                System.out)));
        int a = nextInt();
        int b = nextInt();
        int c = nextInt();
        int[] prime = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
                53, 59, 61, 67, 71, 73, 79, 83, 89, 97 };
        long ans = 0;
        long sum = 0;
        int INF = 1073741824;
        for (int i = 1; i <= a; i++) {
            for (int j = 1; j <= b; j++) {
                for (int j2 = 1; j2 <= c; j2++) {
                    ans = i * j * j2;
                    long res = 1;
                    int k = 0;
                    int tmp = 0;
                    while (ans != 1) {
                        if (ans % prime[k] == 0) {
                            tmp++;
                            ans /= prime[k];
                        } else {
                            res *= (tmp + 1);
                            tmp = 0;
                            k++;
                        }
                    }
                    res *= (tmp + 1);
                    sum += res;
                }
            }
        }
        out.print(sum % INF);
        out.close();
    }
}