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 sun(n):
    if n==1:
        return 1
    else:
        return n+sun(n-1)

def pyr(x):
    l=[]
    i=1
    while sun(i)<=x:
        l.append(sun(i))
        i+=1
    return l

def height(l,n):
    s=int(n)
    r=0
    for i in l:
        if s-i>=0:
            s=s-i
            r+=1
    return r
print(height(pyr(n),n))
