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>
from math import sqrt
def check(temp):
    haha=((temp*(temp+1))*(temp+2))//6
    if(n>=haha):
        return 1
    else:
        return 0
n=int(input())
temp=int(sqrt(n))
lo=1
high=temp+1
while(lo<=high):
    mid=(lo+high)//2
    #print(lo,mid,high)
    if(check(mid)):
        ans=mid
        lo=mid+1
    else:
        high=mid-1
print(ans)