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>
import sys
def main():
    n = int(input()) + 1
    a = [0] * n
    _sum = 0
    for i in range(1, n):
        a[i] = a[i - 1] + i
        _sum += a[i]
        if(_sum > n - 1):
            print(i - 1)
            return
        if(_sum == n - 1):
            print(i)
            return


if __name__ == "__main__":
    sys.exit(main())