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 runprogram():
    # test_cases = open(sys.argv[1], 'r')
    # test_cases = open("uniqueelements.txt", 'r')

    n = int(sys.stdin.readline().rstrip('\n'));

    i = 2
    sum = 0 ;
    count = 0 ;
    while True:
        k = 0
        for j in range(1, i,1):
            k += j
        sum += k
        count += 1 ;
        if  sum == n:
            print count ;
            break;
        elif sum > n:
            print count - 1;
            break;
        i = i + 1

def main():
    runprogram()


main()