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.math.BigInteger;

public class Solution{ 
	
	
	 public static int d(int n){
		 
		 int i,answer=1;
		 int[] a=new int[100];
		 
		 
		 for(i=2;i<=97;i++){
			 while(n%i==0){
				 a[i]++;
				 n/=i;
			 }
		 }
		 
		 for(i=2;i<=97;i++){
			 answer*=(1+a[i]);
		 }
		 
		 return answer;
	 }
	
	 public static void main(String[] args) { 
	     
	     Scanner in = new Scanner(System.in);
	     StringBuilder sb=new StringBuilder();
	     
	     
	     
	     int a,b,c,n,mod,answer=0,i,j,k;
	     
	     mod=1<<30;
	     
	     
	     a=Integer.parseInt(in.next());
	     b=Integer.parseInt(in.next());
	     c=Integer.parseInt(in.next());
	     

	     for(i=1;i<=a;i++){
	    	 for(j=1;j<=b;j++){
	    		 for(k=1;k<=c;k++){
	    			 answer=(answer+d(i*j*k))%mod;
	    		 }
	    	 }
	     }
	     
	     System.out.println(answer);
	     
	     
	 }
}