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.*;
public class B236 {
    public static long mod = 1073741824;
    public static void main(String[] args){
        Scanner br = new Scanner(System.in);
        ArrayList<Integer> primes = new ArrayList<Integer>();
        boolean[] isPrime = new boolean[100];
        Arrays.fill(isPrime, true);
        for(int i = 2;i<100;i++){
            if(isPrime[i]){
                primes.add(i);
                for(int j = i*i;j<100;j+=i){
                    isPrime[j] = false;
                }
            }
        }
        int[][] pfactor = new int[101][primes.size()];
        for(int i = 2;i<101;i++){
            int cur = i;
            for(int j = 0;j<primes.size();j++){
                while(cur%primes.get(j) == 0){
                    pfactor[i][j]++;
                    cur/=primes.get(j);
                }
            }
        }
        int a = br.nextInt();
        int b = br.nextInt();
        int c = br.nextInt();
        long res = 0;
        for(int i = 1;i<=a;i++){
            for(int j = 1;j<=b;j++){
                for(int k = 1;k<=c;k++){
                    long cur = 1;
                    for(int p = 0;p<primes.size();p++){
                        long t = pfactor[i][p]+pfactor[j][p]+pfactor[k][p];
                        t++;
                        cur = cur*t;
                    }
                    res = (res+cur)%mod;
                }
            }
        }
        System.out.println(res);
    }
}
