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>
n = int(input())
def sumof(n):
    return (n * ( n + 1)) // 2
#print(sumof(4))
i = 1
s = 0
count = 0

while s <= n:
    #print('s =',s, 'i  =', i)
    s += sumof(i)
    count += 1
    if s + sumof(i + 1) <= n:
        i += 1
    else:
        break
print(count)
