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 A492_vanyaAndCubes {
		
	public static int cubes (int n ) { 
		if (n == 1 )
			return 1 ; 
	   return (int)(((double)n/2) * (1+n));
	}
	
	public static void main(String[] args) {
		Scanner ss =new Scanner (System.in) ; 
		int  n = ss.nextInt() ; 
		int k = 0 ; 
		int summ = 0 ; 
		for ( int i = 1 ; summ < n ; i ++ ){
			summ+=cubes(i) ; 
			k++ ;
			if (summ > n)
			{
				k--;
			}
	
		}
		System.out.println(k);
	}

}