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.*;

public class EasyNumberChallenge {
	static ArrayList<Integer> prime;
	static Set<Integer> primeset;

	public static void main(String[] args) {
		prime = sieve();
	//	System.out.println(prime);
		primeset = new HashSet<Integer>();
		primeset.addAll(prime);
		Scanner s = new Scanner(System.in);
		int a = s.nextInt();
		int b = s.nextInt();
		int c = s.nextInt();
		long sum = 0;
		
		for (int i = 1; i <= a; i++) {
			for (int j = 1; j <= b; j++) {
				for (int k = 1; k <= c; k++) {
					int mul = i * j * k;
					if (primeset.contains(mul)) {
						sum += 2;
					} else {
						sum += div(i * j * k);
					}
				}
			}
		} 
		System.out.println(sum);

	}

	private static long div(int n) {
		int i = 0;
		int sum = 1;
		while (n > 1) {
		//	System.out.println(i+" "+prime.get(i)+" "+n);
			int count = 0;
			while (n % prime.get(i) == 0) {
				
				n = n / prime.get(i);
		//		System.out.println(n);
				count++;
			}
			if (count > 0) {
				count++;
				sum *= count;
			}
			
			i++;
			
		}

		return sum;
	}

	private static ArrayList sieve() {
		int[] x = new int[1000000];
		x[0] = 1;
		x[1] = 1;
		x[2] = 0;
		for (int i = 4; i < x.length; i += 2) {
			x[i] = 1;
		}
		for (int i = 3; i * i <= x.length; i++) {
			if (x[i] == 0) {
				for (int j = i * i; j < x.length; j += i) {
					x[j] = 1;
				}
			}
		}
		ArrayList<Integer> arr = new ArrayList<>();
		for (int i = 2; i < x.length; i++) {
			if (x[i] == 0) {
				arr.add(i);
			}
		}
		return arr;
	}

}
