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 $2$.