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())
i = 0
m = 0
count = 0
while n > 0:
    count += 1
    m = m + 1
    i += m
    n = n - i
    if n < 0:
        count -= 1
print(count)
# 1 : 1 24
# 2 : 3 21
# 3 : 6 15
# 4 : 10 5
# 5 : 15 -10
# 6 : 21
# 7 : 28

