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())
m=1
M=10**14
mid=(m+M)//2
s=((mid)*(mid+1)//2)
s1=((mid+1)*(mid+2)*(mid+3)//6)
while not (s<=n and s1>n):
    mid=(m+M)//2
    s=((mid)*(mid+1)*(mid+2)//6)
    s1=((mid+1)*(mid+2)*(mid+3)//6)
    if s<n and s1<n:
        m=mid
    elif s>n:
        M=mid
    else:
        break
if s1>n:
    print(mid)
else:
    print(mid+1)