From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the first question(Carried 20 marks out of 100) for the Round 2 of 2013 hacker cup.

Problem Statement

“Happy birthday to you… Happy birthday to you… Happy birthday to Grovyle… Happy birthday to you…”

Today is Grovyle’s birthday and he is going to invite his friends to his birthday party. To have an awesome party, each of the attendants should get one piece of cake. Your job is to help Grovyle invite as many friends as you can.

However, Grovyle’s parents are very mean, and make him use the following rules when cutting his cake:

• There is only ONE cylindrical cake.
• Grovyle cuts the cake N times, each cut being perpendicular to the surface of the cake.
• The i-th cut is a broken line with a[i] vertices.
• The knife is only allowed to intersect the edge of the cylindrical cake at the start and end of the cut.What is the maximum number of pieces Grovyle could get?
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From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the first question in the qualification round of 2013 hacker cup.

When John was a little kid he didn’t have much to do. There was no internet, no Facebook, and no programs to hack on. So he did the only thing he could… he evaluated the beauty of strings in a quest to discover the most beautiful string in the world.

Given a string s, little Johnny defined the beauty of the string as the sum of the beauty of the letters in it.

The beauty of each letter is an integer between 1 and 26, inclusive, and no two letters have the same beauty. Johnny doesn’t care about whether letters are uppercase or lowercase, so that doesn’t affect the beauty of a letter. (Uppercase ‘F’ is exactly as beautiful as lowercase ‘f’, for example.)

You’re a student writing a report on the youth of this famous hacker. You found the string that Johnny considered most beautiful. What is the maximum possible beauty of this string?

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