CF36C.Bowls

Once Petya was in such a good mood that he decided to help his mum with the washing-up. There were n dirty bowls in the sink. From the geometrical point of view each bowl looks like a blunted cone. We can disregard the width of the walls and bottom. Petya puts the clean bowls one on another naturally, i. e. so that their vertical axes coincide (see the picture). You will be given the order in which Petya washes the bowls. Determine the height of the construction, i.e. the distance from the bottom of the lowest bowl to the top of the highest one.

有一次，佩蒂亚心情特别好，决定帮妈妈洗碗。水槽里有 $n$ 个脏碗。从几何角度看，每个碗的形状都类似于一个截头圆锥（即圆台）。我们可以忽略碗壁和碗底的厚度。佩蒂亚将洗净的碗自然地一个叠在另一个上面，即让它们的竖直轴线重合（见图）。你将获知佩蒂亚洗碗的顺序。请计算这一叠碗的总高度，即从最底部碗的底面到最顶部碗的顶面之间的距离。

The first input line contains integer n (1 ≤ n ≤ 3000). Each of the following n lines contains 3 integers h, r and R (1 ≤ h ≤ 10000, 1 ≤ r < R ≤ 10000). They are the height of a bowl, the radius of its bottom and the radius of its top. The plates are given in the order Petya puts them on the table.

第一行输入包含一个整数 $n$（$1 \leq n \leq 3000$）。接下来的 $n$ 行每行包含三个整数 $h$、$r$ 和 $R$（$1 \leq h \leq 10000$，$1 \leq r < R \leq 10000$），分别表示一个碗的高度、底部半径和顶部半径。这些碗按小彼佳将它们放置到桌面上的顺序给出。

Output the height of the plate pile accurate to at least 10 - 6.

输出板桩的高度，精确到至少 $10^{-6}$。