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: 

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#!/usr/bin/env python2

def compare(int_num_a, int_num_b):
    if int_num_a == int_num_b:
        return 0
    elif int_num_a > int_num_b:
        return 1
    else:
        return -1


BEGIN_N = 1
END_N   = 10001

n = input()
cubes_cnt_sum = cubes_cnt_current_level = 0
for level in range(BEGIN_N, END_N):
    cubes_cnt_current_level += level
    cubes_cnt_sum           += cubes_cnt_current_level
    result = compare(cubes_cnt_sum, n)
    if 0 == result:
        print level
        break
    elif 1 == result:
        print level - 1
        break