Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + ... + (i - 1) + i cubes.

Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input

The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Examples

Input

1


Output

1


Input

25


Output

4

Note

Illustration to the second sample: 

<image>
import java.text.DecimalFormat;
import java.util.Scanner;
 
public class BuoiHocThu1 {
 
	public static void main(String[] args) {
		DecimalFormat df = new DecimalFormat("0");
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int count = 1, sum = 0;
		for(;;) {
			int tempt = 0;
			int i =1;
			for(; i <= count; ++i) {
				tempt +=i;
			}
			sum+=tempt;
			if(sum==a) {
				System.out.println(i-1);
				break;
			}
			else if (sum>a) {
				System.out.println(i-2);
				break;
			}
			++count;
		}
		sc.close();
	}
}