The $k\text{th}$ equilateral number is obtained by taking the sum of the first $k$ positive integers. For example, the $5$th equilateral number is $1+2+3+4+5=15$.

Given a positive integer $n$, you want to represent it as a sum of equilateral numbers. How many numbers do you need at least?

Input

The only line of the input contains the integer $n$.

Output

Output the smallest amount of equilateral numbers whose sum is $n$.

Constraints

• $1 \le n \le 10^{12}$

Example

Input:

5

Output:

3

Explanation: You need at least three equilateral numbers (you can choose $1$, $1$, and $3$).