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
from fractions import Fraction as frac

MOD = 1e9 + 7

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)

def lcm(a, b):
    return a * b // gcd(a, b)

def no():
    print("NO")
    return

def yes():
    print("YES")
    return

def solve(case_no):
    n = int(input())
    for i in range(1, 10000):
        n -= i * (i + 1) // 2
        if n < 0:
            print(i - 1)
            exit()

t = 1
# t = int(input())
for i in range(1, t + 1):
    solve(i)
