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.io.*;
import java.util.*;

public class EasyNumberChallenge {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int a = Integer.parseInt(st.nextToken());
        int b = Integer.parseInt(st.nextToken());
        int c = Integer.parseInt(st.nextToken());
        int mod = 1073741824;
        int sum = 0;    
        int[] arr = new int[1000001];
        Arrays.fill(arr, -1);
        for (int i = 1; i <= a; i++)
            for (int j = 1; j <= b; j++)
                for (int k = 1; k <= c; k++)
                {
                    int d;
                    if (arr[i*j*k] == -1)
                    {
                        d = d(i*j*k);
                        arr[i*j*k] = d;
                    }
                    else
                        d = arr[i*j*k];
                    sum = (sum + d) % mod;
                }
                    
        System.out.println(sum);
    }
    
    public static int d(int n)
    {
        int count = 0;
        int i = 1;
        for (i = 1; i*i <= n; i++)
            if (n%i == 0)
                count += 2;
        if ((i-1)*(i-1) == n)
            count--;
        return count;
    }
}