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.util.*;
import java.io.*;

public class ndaidemf {
	public static void main(String[] args) {
		new ndaidemf();
	}
	
	ndaidemf() {
		Scanner s = new Scanner(System.in);

		int MAX = 1000100;
		int[] cnt = new int[MAX];
		
		int a = s.nextInt();
		int b = s.nextInt();
		int c = s.nextInt();
		int res = 0;
		int MOD = 1<<30;
		
		for(int i = 1; i <= a; i++) {
			for(int j = 1; j <= b; j++) {
				for(int k = 1; k <= c; k++) {
					int t = i * j * k;
					if(cnt[t] == 0) {
						for(int ii = 1; ii * ii <= t; ii++) {
							if(t % ii == 0) {
								cnt[t]++;
								if(t / ii != ii) cnt[t]++;
							}
						}
					}
					res += cnt[t];
					if(res >= MOD) res -= MOD;
				}
			}
		}
		
		System.out.println(res);
	}

}