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:

<image>

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.*;

/**
 * @author Muhammad Magdi
 * 0    1   2   3   4
 *
 */

/*
012345678
ababaabab
*/
public class Main {

		public static int numDivs(int n){
			int ret = 0, i;
			for(i = 1 ; i*i < n ; ++i){
				if(n%i == 0)	ret += 2;
			}
			if(i*i == n)	++ret;
			return ret;
		}

		public static int [] sieve(int n){
			int [] numDivs = new int [n];
			Arrays.fill(numDivs, 1);
			for(int i = 2 ; i < n ; ++i){
				if(numDivs[i] == 1){
					for(int j = i ; j < n ; j+=i){
						int e = 0, t = j;
						while(t%i == 0){
							t /= i;
							++e;
						}
						numDivs[j] *= (e+1);
					}
				}
			}
			return numDivs;
		}

    public static void main(String[] args) throws java.lang.Exception{
        MyScanner in = new MyScanner();
        PrintWriter out = new PrintWriter(System.out);
				int a = in.nextInt(), b = in.nextInt(), c = in.nextInt();
				int ans = 0, mod = 1<<30;
				int [] numDivs = sieve(1000009);
				for(int i = 1 ; i <= a ; ++i){
					for(int j = 1 ; j <= b ; ++j){
						for(int k = 1 ; k <= c ; ++k){
							ans = (ans%mod + numDivs[i*j*k]%mod)%mod;
						}
					}
				}
				out.println(ans);
        out.close();
    }

    static class MyScanner{
        StringTokenizer st;
        BufferedReader br;
        public MyScanner(){br = new BufferedReader(new InputStreamReader(System.in));}
        public MyScanner(FileReader s) throws FileNotFoundException {	br = new BufferedReader(s);}
        public String next() throws IOException{
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public long nextLong() throws IOException {return Long.parseLong(next());}
        public String nextLine() throws IOException {return br.readLine();}
        public double nextDouble() throws IOException { return Double.parseDouble(next()); }
        public boolean ready() throws IOException {return br.ready();}
    }
}