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>
koll_kybikov = int(input())
##данные для арифметической прогрессии
Summa_progressii = 0
last_znach = 0
d = 1
pervoe_znachenie = 1
n = last_znach

koll_ryad = 0
Summa_kubikov_v_piramide = 0

##    цикл для нахождения арифметической прогрессии
while Summa_progressii < koll_kybikov :   
    last_znach = last_znach + 1
    n = last_znach                
    Summa_progressii = (pervoe_znachenie + last_znach)/2 * n
    

    if (Summa_kubikov_v_piramide + Summa_progressii)    >  koll_kybikov :
        break
    Summa_kubikov_v_piramide = Summa_kubikov_v_piramide + Summa_progressii
     
    
##нахождение колличества рядов в пирамиде
     
    koll_ryad = koll_ryad + 1
print(koll_ryad)  
