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.util.Scanner;


public class Expressions {

	/**
	 * @param args
	 */ 
	public static void main(String[] args) {
			Scanner sc = new Scanner(System.in);
			
			int n = sc.nextInt();
			int i = 1;
			int j = 1;
			if(n == 1) System.out.println("1");
			else
			{
				while(n>=j)
					{   
				j = j + i;
				n = n - (j);	
				i++;
				//System.out.println(j);

			}
				System.out.println(i-1);
			}
			
			
			
			
	}
}
