35009번 - Largest Area 스페셜 저지다국어

문제

You are given a rectangle on the plane with vertices at integer points. Calculate the area of the largest ellipse that can fit entirely within this rectangle. Recall that a rectangle is a convex quadrilateral with all right angles, and an ellipse is a figure on the plane defined by two focal points $F_1$ and $F_2$ (not necessarily with integer coordinates; possibly $F_1 = F_2$) and a real number $d > |F_1 F_2|,ドル consisting of points $P$ on the plane such that $|F_1 P| + |F_2 P| \le d$.

입력

You are given a rectangle on the plane with vertices at integer points. Calculate the area of the largest ellipse that can fit entirely within this rectangle. Recall that a rectangle is a convex quadrilateral with all right angles, and an ellipse is a figure on the plane defined by two focal points $F_1$ and $F_2$ (not necessarily with integer coordinates; possibly $F_1 = F_2$) and a real number $d > |F_1 F_2|,ドル consisting of points $P$ on the plane such that $|F_1 P| + |F_2 P| \le d$.

출력

Output a single real number: the largest area of an ellipse that can be drawn inside the rectangle given in the input. The answer is considered correct if its relative or absolute error does not exceed 10ドル^{-6}$.

제한

노트