Artistic Souvenir

A typical circular design on a square Delft tile.

Delft is world-famous for its blue and white pottery (also known as Delfts blauw), and the earliest pieces date back to the 16th century.

During a stroll in Delft, Christiaan sees a lot of beautifully painted pottery objects like plates, tiles, and vases in the souvenir shops. Inspired by those, he decides to hand paint such a square tile himself. He has already picked a circular design he wants to place in the middle of the tile. He would like to leave a margin of at least $1 \text{cm}$ around the design. Now, Christiaan just needs to buy a square tile of a suitable size.

Given the area of the circular design, what is the minimum area of the square tile?

The input consists of:

• One line with an integer $a$ ($1 \leq a\leq 10^{15}$), the area of the circular design in $\text{cm}^2$.

Output the minimum area of the square tile in $\text{cm}^2$ that is needed for a design with area $a$ if Christiaan wants to leave a margin of at least $1 \text{cm}$ around the design.

Your answer should have an absolute or relative error of at most $10^{-9}$.