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>
# -*- coding: utf-8 -*-
n = int(raw_input())

result = 0


def progression_sum(_n):
    # print('Progression for {}'.format(_n))
    if _n == 1:
        return 1.0
    return (1 + _n) / 2.0 * _n


for i in xrange(n):
    row = progression_sum(i+1)
    # print('Row: {}'.format(row))
    n -= row
    if n >= 0:
        result += 1
    else:
        break
print(result)
