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* ≤ 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.

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 .

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