Solve the programming task below in a Python markdown code block.
There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0. During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right. That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i. The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible. Find the earliest possible time to reach coordinate X.

Constraints

* X is an integer.
* 1≤X≤10^9

Input

The input is given from Standard Input in the following format:


X


Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Examples

Input

6


Output

3


Input

2


Output

2


Input

11


Output

5