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.*;


import java.lang.*;
import java.math.BigInteger;
import java.io.*;
public class Main{
	public static void main (String[] args) throws java.lang.Exception{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int rowNum = 1, num = 2;
		int height = 0;
		while(n >= rowNum){
			n -= rowNum;
			height ++;
			rowNum = rowNum + num;
			num ++;
		}
		System.out.println(height);
		scan.close();
	}
}