A10188. 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.

The first line of the input contains a single integer $n$ ( $1<=n<=100000)$ — the number of simple cakes Babaei has.

Each of the following $n$ lines contains two integers $r_{i}$ and $h_{i}$ ( $1<=r_{i},h_{i}<=10000$ ), giving the radius and height of the $i$ -th cake.

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 .

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 $4$ .