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.*;
import java.lang.Math;

public class Solution{
    static int[] mem;
    public static void main(String[] args){
        Scanner s = new Scanner(System.in);
        int a = s.nextInt();
        int b = s.nextInt();
        int c = s.nextInt();
        int answer = 0;
        mem = new int[a*b*c +1];
        for(int i = 1; i <= a; i++){
            for(int j = 1; j <= b; j++){
                for(int k = 1; k <= c; k++){
                    answer += help(i*j*k);
                    answer %= 1073741824;
                }
            }
        }
        
        System.out.println(answer);
    }
    
    public static int help(int n){
        if(n==1)return 1;
        if(mem[n] != 0) return mem[n];
        double ss = Math.sqrt(n);
        int s = (int)(ss);
        int answer = 0;
        for(int i = 1; i <= s; i++){
            if(n%i==0) answer += 2;
        }
        if(s == ss) answer--;
        mem[n] = answer;
        return answer;
    }
}