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 VanyaAndCubesTest {

	public static void main(String[] args) {
		
		Scanner in = new Scanner(System.in);
		int n;
		
		try{
			n = in.nextInt();
		}finally{
			in.close();
		}
		
		if(n == 1){
			System.out.println(1);
			return;
		}
		
		int height = 1;
		while(getTotalCount(height) <= n){
			height++;
		}
		
		System.out.println(height - 1);
	}
	
	public static int getTotalCount(int h){
		return (h*h*(h+1))/2 - (h*(h-1)*(h+1))/3;
	}

}