Nick has bought a fog machine for Halloween and is helping organize a party where the fog machine will be used to set the mood.

To operate the fog machine, Nick initializes it with a positive integer ~v_{init}~. The fog that comes out of the machine then moves as follows:

• The initial upward velocity of the fog is ~v_{init}~, and the initial ~y~-coordinate of the fog is ~0~.
• While the fog has positive upward velocity, simulate the following steps in order:
  1. Increase the ~y~-coordinate of the fog by the upward velocity.
  2. Decrease the upward velocity by ~1~.
• After this point, the fog has reached its maximum height.

There is a smoke detector at ~y = y_0~ that will go off if fog reaches a ~y~-coordinate greater than or equal to that of the smoke detector.

Compute the largest possible value of ~v_{init}~ that Nick can initialize the fog machine to without setting off the smoke detector.

Constraints

~2 \le y_0 \le 10^5~

Input Specification

The first and only line of input contains a positive integer ~y_0~.

Output Specification

Output the maximum possible integer value of ~v_{init}~. It can be shown that, under the constraints of the problem, the answer is always a finite positive integer.

Sample Input 1

3

Sample Output 1

1

Sample Explanation 1

If ~v_{init}~ is set to ~1~, the maximum height the fog reaches is ~1~. However, if ~v_{init}~ is set to ~2~, the maximum height the fog reaches is ~3~. Therefore, the answer is ~1~.

Sample Input 2

4

Sample Output 2

2

Sample Explanation 2

If ~v_{init}~ is set to ~2~, the maximum height the fog reaches is ~3~. However, if ~v_{init}~ is set to ~3~, the maximum height the fog reaches is ~6~. Therefore, the answer is ~2~.