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.Scanner;

public class Easy_Number_Challange {
	static int d = 1073741824;
	static boolean[][][] visited ;
	static int[] dp;
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int a = scan.nextInt();
		int b = scan.nextInt();
		int c = scan.nextInt();
		visited = new boolean[a+1][b+1][c+1];
		dp = new int[a * b *c + 1];
		
		System.out.println(solve(a,b,c));
	}
	
	static int countDivisors(int n) 
    { 
        int cnt = 0; 
        for (int i = 1; i <= Math.sqrt(n); i++) 
        { 
            if (n % i == 0) { 
                if (n / i == i) 
                    cnt++; 
  
                else 
                    cnt = cnt + 2; 
            } 
        } 
        return cnt; 
    }
	
	static int solve(int a , int b , int c) {
		if (a == 0 || b == 0 || c == 0)
			return 0;
		if (visited[a][b][c])
			return 0;
		else {
			visited[a][b][c] = true;
			if (dp[a*b*c] != 0)
				return  (dp[a*b*c] % d + solve(a-1,b,c)%d + solve(a,b-1,c)%d + solve(a,b,c-1)%d) % d;
			int sum = (countDivisors(a * b *c) % d);
			dp[a*b*c] = sum%d;
			return (sum + solve(a-1,b,c)%d + solve(a,b-1,c)%d + solve(a,b,c-1)%d) % d;
		}
	}

}
