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>
num = input()
num = int(num)
if num > 0 and num < 10001:
    ctrht = 0
    total = 0
    while True:
        ctrht +=1
        ctr = 0
        while ctrht >= ctr:
            total += ctr
            ctr+= 1
            
        if total > num:
            break
        
        
    print(ctrht-1)
        
else:
    print('Invalid input')
