CF157B.Trace

One day, as Sherlock Holmes was tracking down one very important criminal, he found a wonderful painting on the wall. This wall could be represented as a plane. The painting had several concentric circles that divided the wall into several parts. Some parts were painted red and all the other were painted blue. Besides, any two neighboring parts were painted different colors, that is, the red and the blue color were alternating, i. e. followed one after the other. The outer area of the wall (the area that lied outside all circles) was painted blue. Help Sherlock Holmes determine the total area of red parts of the wall.

Let us remind you that two circles are called concentric if their centers coincide. Several circles are called concentric if any two of them are concentric.

一天，夏洛克·福尔摩斯在追捕一名极其重要的罪犯时，发现墙上挂着一幅精美的画作。这面墙可被视作一个平面。画作由若干个同心圆构成，将墙面划分成了若干区域。其中一些区域被涂成红色，其余区域则被涂成蓝色。此外，任意两个相邻区域的颜色均不相同，即红色与蓝色交替出现。墙面最外侧的区域（即位于所有圆之外的区域）被涂成蓝色。请帮助夏洛克·福尔摩斯计算墙面中所有红色区域的总面积。

需要提醒您：若两个圆的圆心重合，则称它们为同心圆；若若干个圆中任意两个均为同心圆，则称这些圆为同心圆。

The first line contains the single integer n (1 ≤ n ≤ 100). The second line contains n space-separated integers r__i (1 ≤ r__i ≤ 1000) — the circles' radii. It is guaranteed that all circles are different.

第一行包含一个整数 $n$（$1 \leq n \leq 100$）。第二行包含 $n$ 个用空格分隔的整数 $r_i$（$1 \leq r_i \leq 1000$）——各圆的半径。保证所有圆互不相同。

Print the single real number — total area of the part of the wall that is painted red. The answer is accepted if absolute or relative error doesn't exceed 10 - 4.

输出一个实数——墙壁上被涂成红色的部分的总面积。若绝对或相对误差不超过 $10^{-4}$，则答案视为正确。

In the first sample the picture is just one circle of radius 1. Inner part of the circle is painted red. The area of the red part equals π × 12 = π.

In the second sample there are three circles of radii 1, 4 and 2. Outside part of the second circle is painted blue. Part between the second and the third circles is painted red. Part between the first and the third is painted blue. And, finally, the inner part of the first circle is painted red. Overall there are two red parts: the ring between the second and the third circles and the inner part of the first circle. Total area of the red parts is equal (π × 42 - π × 22) + π × 12 = π × 12 + π = 13π

在第一个样例中，图形仅是一个半径为 $1$ 的圆，圆的内部区域被涂成红色。红色区域的面积为 $\pi \times 1^2 = \pi$。

在第二个样例中，共有三个半径分别为 $1$、$4$ 和 $2$ 的圆。第二个圆的外部区域被涂成蓝色；第二个圆与第三个圆之间的环形区域被涂成红色；第一个圆与第三个圆之间的区域被涂成蓝色；最后，第一个圆的内部区域被涂成红色。总体而言，共有两个红色区域：第二个圆与第三个圆之间的环形区域，以及第一个圆的内部区域。红色区域的总面积为 $(\pi \times 4^2 - \pi \times 2^2) + \pi \times 1^2 = \pi \times 12 + \pi = 13\pi$。