CF629D.Babaei and Birthday Cake

As you know, every birthday party has a cake! This time, Babaei is going to prepare the very special birthday party's cake.

Simple cake is a cylinder of some radius and height. The volume of the simple cake is equal to the volume of corresponding cylinder. Babaei has n simple cakes and he is going to make a special cake placing some cylinders on each other.

However, there are some additional culinary restrictions. The cakes are numbered in such a way that the cake number i can be placed only on the table or on some cake number j where j < i. Moreover, in order to impress friends Babaei will put the cake i on top of the cake j only if the volume of the cake i is strictly greater than the volume of the cake j.

Babaei wants to prepare a birthday cake that has a maximum possible total volume. Help him find this value.

众所周知，每场生日派对都少不了蛋糕！这一次，Babaei 将要为这场特别的生日派对准备一款非常特别的蛋糕。

一个普通蛋糕是一个具有特定半径和高度的圆柱体。普通蛋糕的体积等于对应圆柱体的体积。Babaei 有 $ n $ 个普通蛋糕，他计划通过将若干个圆柱体上下叠放来制作这款特别的蛋糕。

然而，这里还有一些额外的烹饪限制：这些蛋糕被编号为 $ 1, 2, \dots, n $，其中编号为 $ i $ 的蛋糕只能直接放在桌子上，或放在编号为 $ j $ 的蛋糕上，且必须满足 $ j < i $。此外，为了给朋友们留下深刻印象，Babaei 仅当蛋糕 $ i $ 的体积严格大于蛋糕 $ j $ 的体积时，才会将蛋糕 $ i $ 放在蛋糕 $ j $ 的上方。

Babaei 希望制作出总体积尽可能大的生日蛋糕。请帮助他找出这个最大可能的总体积。

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of simple cakes Babaei has.

Each of the following n lines contains two integers r__i and h__i (1 ≤ r__i, h__i ≤ 10 000), giving the radius and height of the i-th cake.

输入的第一行包含一个整数 $n$（$1 ≤ n ≤ 100\,000$）—— Babaei 拥有的简单蛋糕的数量。

接下来的 $n$ 行中，每行包含两个整数 $r_i$ 和 $h_i$（$1 ≤ r_i,\,h_i ≤ 10\,000$），分别表示第 $i$ 个蛋糕的半径和高度。

Print the maximum volume of the cake that Babaei can make. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if .

输出 Babaei 能够制作的蛋糕的最大体积。若您的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

即：假设您的答案为 $a$，评测组的答案为 $b$。当满足 $\frac{|a-b|}{\max(1,|b|)} \leq 10^{-6}$ 时，评测程序将判定您的答案正确。

In first sample, the optimal way is to choose the cake number 1.

In second sample, the way to get the maximum volume is to use cakes with indices 1, 2 and 4.

在第一个样例中，最优方案是选择编号为 1 的蛋糕。

在第二个样例中，获得最大体积的方法是使用编号为 1、2 和 4 的蛋糕。