Cake
Description
Recently, after creating a surplus amount of milk, Bessie has decided to create a cake! She creates a square cake with dimensions $N$ and $N$. However, Farmer John is forcing her to share the cake with Elsie. Farmer John wants Bessie to create a permutation of $0…N$, which she will use to cut the cake by basing the height of the cut-off on the permutation. For example, if the permutation was $0 2 1 3$, Bessie would start off at a height of zero on the left of the cake. Then she will move up to $2$ for the next cut, then $1$, then finally finish at $3$ on the right of the cake. Here is an image describing the outcome of the previous permutation.
Bessie will get the bottom portion of the cake, while Elsie will get the top. Find the maximum area Bessie can obtain.
The first line contains a single integer $N (1≤N≤2⋅10^5)$, the dimensions of the cake.
Output a single number, the maximum area Bessie can obtain. Your answer will be accepted if the absolute or relative error does not exceed $10^{−9}$. Formally, let your answer be $a$, and the jury's answer be $b$. Your answer is considered correct if $\frac{|a - b|}{max(1, |b|)} \le 10^{-9}$.
Input
The first line contains a single integer $N (1≤N≤2⋅10^5)$, the dimensions of the cake.
Output
Output a single number, the maximum area Bessie can obtain. Your answer will be accepted if the absolute or relative error does not exceed $10^{−9}$. Formally, let your answer be $a$, and the jury's answer be $b$. Your answer is considered correct if $\frac{|a - b|}{max(1, |b|)} \le 10^{-9}$.