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>
end_n = 10001

cubes_cnt_of_current_level = 0
cubes_sum_until_current_level = [0,]
for level in range(1, end_n):
    cubes_cnt_of_current_level += level
    cubes_sum_until_current_level.append(cubes_sum_until_current_level[level - 1] + cubes_cnt_of_current_level)
    if (cubes_sum_until_current_level[level] >= end_n):
        break

level_end = len(cubes_sum_until_current_level)
n = input()
for i in range(1, level_end):
    if (cubes_sum_until_current_level[i] > n):
        print i - 1
        break
else:
    print level_end - 1