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 ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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.
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class EasyNumberChallenge {

    static int _sieve_size;
    static int modulo = 1073741824;

    static ArrayList<Integer> primes = new ArrayList<Integer>();
    static boolean[] bs;

    static void sieve(int upperbound) {
        _sieve_size = upperbound + 1;
        bs = new boolean[_sieve_size];
        Arrays.fill(bs, true);
        bs[0] = bs[1] = false;
        for (long i = 2; i < _sieve_size; i++)
            if (bs[(int) i]) {
                for (long j = i * i; j < _sieve_size; j += i)
                    bs[(int) j] = false;
                primes.add((int) i);
            }
    }

    static long numDiv(long N) {
        int PF_idx = 0;
        long PF = primes.get(PF_idx), ans = 1;
        while (N != 1 && (PF * PF <= N)) {
            long power = 0;
            while (N % PF == 0) {
                N /= PF;
                power++;
            }
            ans *= (power + 1);
            PF = primes.get(++PF_idx);
        }
        if (N != 1)
            ans *= 2;
        return ans;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        int c = sc.nextInt();
        long divs[] = new long[(a * b * c) + 1]; 
        sieve((a*b*c) + 1);
        for (int i = 1; i < divs.length; i++) {
            divs[i] = numDiv(i);
        }

        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 = sum + divs[i * j * k] % modulo;
                }
            }
        }
        System.out.println(sum % modulo);

    }
}
