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 preprocess():
    index_array = [0 for _ in range(0, 200)]
    index_array[0] = 1
    

    for i in range(1, 200):
        index_array[i] = index_array[i-1] + (i+1)

    sum_array = [_ for _ in index_array]

    for i in range(1, 100):
        sum_array[i] += sum_array[i-1]
    
    return sum_array


def main(num):
    sum_array = preprocess()

    for i in range(0, len(sum_array)):
        if sum_array[i] > num:
            return i


if __name__ == '__main__':

    print main(input())
