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50508 - The Biggest Area

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

The Biggest Area

You are given the information about 3 different shapes: Ellipse, Trapezoid and Hexagon.

Question: Find the total area for n shapes and the type of the shape with the biggest area.

Note: Use 3.14159 for PI and 1.732 for sqrt(3).

Input specification
You will be given an integer in the beginning: the number of shapes (n) where n is less than 2500. Then in the following n lines, you will be given information for n shapes:

  1. Type of the shape
    1. Ellipse
    2. Trapezoid
    3. Hexagon
  2. If ellipse is given, you will be given two integers a and b. If trapezoid is given you will be given 3 integers: a, b, h. Otherwise you will be given one integer (a)

Output specification
Show two information: 1) Total area for n shapes (two digits precision) and 2) The type of the shape with the biggest area

Sample Input I
4
3 8
3 6
1 3 7
2 2 10 10
Sample Output I
385.773 3

Explanation:
There are 4 shapes given

  1. Shape 1 is a Hexagon and its area is 166.272. And it's the biggest shape among the given.
  2. Shape 2 is also a Hexagon with an area of 93.528.
  3. Shape 3 is an Ellipse with an area of 65.973.
  4. Shape 4 is a Trapezoid with an area of 60.
So, the total area is 385.773 (166.272+93.528+65.973+60)


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