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>

from math import factorial as fct

def ps(n,m):
	return int(fct(n)/(fct(m)*fct(n-m)))

def cl(n):
	return ps(n+2,3)

def cdt(n):
	dt=dict()
	for x in range(n):
		x+=1
		dt[cl(x)]=x
	return dt

def dl(dt,n):
	v=list(dt.keys())
	for x in range(len(v)):
		if v[x+1] > n:
			return v[x]

dt=cdt(39)
l=dl(dt,int(input()))
print(dt[l])
