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 math
def cubeSeries(n):
    series = []
    prev = 0
    for i in range(1,n+1):
        cur = prev+sum([i for i in range(1,i+1)])
        series.append(cur)
        prev = cur
    return series

c = input()
n1 = (-1+math.sqrt(1+4*c))/2
n2 = (-1-math.sqrt(1+4*c))/2
prob =  int(round(n1))
series = cubeSeries(prob+1)
ans = 1
for i in range(len(series)-1):
    if(c<series[i+1] and c>=series[i]):
        ans = i+1
        break
    if(c == series[i+1]):
        ans= i+2
        break
print ans