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 main():
	num = int(input())
	pyramid = []
	pyramid.append(1)
	levelBlocks = 1
	totalBlocks = 1
	levels = 1
	curr = 2
	while True:
		if num <= totalBlocks:
			break
		levelBlocks += curr
		totalBlocks += levelBlocks
		curr += 1
		levels+= 1
		if num < totalBlocks:
			levels-=1
			break

	print(levels)


main()
