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>
def f(n):
    return n*(n+1)*(n+2)/6

if __name__ == '__main__':
    n=int(input())
    if n<=20:
        a=1
        b=4
    else:
        c=n*6
        r=int(c**(1/3))
        a=r-2
        b=r+2
    i=b
    while f(i)>n:
        i-=1
    print(int(i))
        
