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.*;
import java.util.*;

import java.util.StringTokenizer;


public class CodeForce {

    public static void main(String[] args) throws IOException{
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
            
        int a = in.nextInt() ; 
        int b = in.nextInt() ; 
        int c = in.nextInt() ; 
        int mem[] = new int [1000001]  ;
 
        
        
      
        int answer = 0 ; 
        for(int x = 1 ; x<=a ;++x){
            for(int y = 1 ; y<=b ;++y){
                for(int z = 1 ; z<=c ;++z){
                    int temp  = x*y*z ;
                    if(mem[temp]==0){
                        int divisorsTemp=findDivisors(x*y*z);
                        mem[temp] = divisorsTemp;
                    answer+=divisorsTemp;
                    }
                    else{
                        answer+=mem[temp];
                    }
                }
            }
        }

        
        out.println(answer%1073741824 );
        out.close();
// 
//          

    }
         
   
    
    private static int findDivisors(int number){
        int divisors = 2 ;
        if (number == 1 ){
            return 1 ;
        }
    for(int i=2 ; i*i <=number ; ++i){
        if(number%i==0){
            if((number/i)==i){
                ++divisors;
            }else{
                divisors+=2;
            }
        }
    }
      return divisors ;
    }

}

                

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
}