Marble Pyramid Levels

You are given an integer (n) representing the number of marbles. Your task is to determine the maximum number of complete levels of a pyramid that can be built using these marbles, where the (i)-th level requires exactly (i) marbles. In other words, you need to find the largest integer (k) such that

[ 1 + 2 + \cdots + k \le n, \quad \text{or} \quad \frac{k(k+1)}{2} \le n. ]

If there are not enough marbles to build even the first level, output 0.

Example:
For (n = 15), the maximum number of complete levels is 5 because (1 + 2 + 3 + 4 + 5 = 15).

inputFormat

The input consists of a single integer (n) denoting the number of marbles. Read the input from stdin.

outputFormat

Output a single integer representing the maximum number of complete levels that can be constructed, printed to stdout.## sample

15

5