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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class numberchallenge {

	public static BufferedReader read = null;
	public static PrintWriter out = null;
	public static StringTokenizer token = null;

	
	public static void solve() {
		
		long mod = 1l << 30;
		int max = 100*100*100;
		int d[] = new int[max+1];
		for(int i = 1; i <= max; i++) {
			for(int j = i; j <= max; j += i) {
				d[j]++;
			}
		}
		int a = nint();
		int b = nint();
		int c = nint();
		long sum = 0;
		for(int i = 1; i <= a; i++) {
			for(int j = 1; j <= b; j++) {
				for(int k = 1; k <= c; k++) {
					sum += d[i*j*k] % mod;
				}
			}
		}
		out.println(sum % mod);
	}


	public static void main(String[] args) {

		read = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		out.close();
	}

	//io functions
	public static String next() {
		while(token == null || !token.hasMoreTokens()) {
			try {
				token = new StringTokenizer(read.readLine());
			} catch(IOException e) {
				e.printStackTrace();
			}
		}
		return token.nextToken();
	}

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

	public static long nlong() {
		return Long.parseLong(next());
	}

	public static double ndouble() {
		return Double.parseDouble(next());
	}

	public static int[] narr(int n) {
		int[] a = new int[n];
		for(int i = 0; i < n; i++)  a[i] = nint();
		return a;
	}

	public static long[] nal(int n) {
		long[] a = new long[n];
		for(int i = 0; i < n; i++) a[i] = nlong();
		return a;
	}
}