# DCP-370: Couple Land Back to All Problems

Easy Math > Basic Math

Mishuk a MO (Math Olympiad) contestant has just arrived on Park with his younger brother Monir for some refreshment. First time for Monir. To arrive here he has been so much surprised to see the environment of Park. <br/> <br/> Monir: Oh My God !! Couple, couple and couple. Is it a park or couple land, bro ? <br/> Mishuk: No, it is a Park, bro. <br/> Monir: Are you sure? <br/> Mishok: Definitely. <br/> Mishok: Well, I have remember a problem to see that environment. <br/> Monir: What type of problem ? <br/> Mishuk: Easy problem. <br/> Monir: Please tell me. <br/> Mishuk: Do you know about the couple ? <br/> Monir: Sure. <br/> Monir: It contains always two something. <br/> Mishok: Okay, my problem is....<br/><br/>Suppose you have N people, among them Odd numbers are representing Girls and Even numbers are representing the Boys and you know about the valid couple, it will be always (odd, even) or (even, odd) combination. Mind it, a cloned person or any homogeneous can not be a part of couple like (odd, odd) or (even, even). <br/> Now you have to tell that how many couple are possible from 1 to N people ? <br/> [Monir is thinking and thinking …..] <br/> <br/> Can you help Monir ? Note: All pairs must be pairwise different. See the explanation for more details. Input: ------ First there is an integer **T (1<=100)**, denoting the number of test cases. Each case contains an integer **N (1 ≤ N ≤ 10<sup>9</sup>)** denoting the number of People. Output: ------- For each case of input, Print "Case X: Y" where "X" is the case number and "Y" is the desired result which means possible couple can be built for N people according to above conditions. Here indexes are 1 based. Sample Input ------------ 3 5 6 7 Sample Output ------------- Case 1: 6 Case 2: 9 Case 3: 12 **Analysis:** <br/> *for the first test from 1 to 5, valid couples are (1, 2); (1, 4); (2, 3); (2, 5); (3, 4); (4, 5); <br/> for the second test valid couples are (1, 2); (1, 4); (1, 6); (2, 3); (2, 5); (3, 4); (3, 6); (4, 5); (5, 6); <br/> for the third valid couples are (1, 2); (1, 4); (1, 6); (2, 3); (2, 5); (2, 7); (3, 4); (3, 6); (4, 5); (4, 7); (5, 6); (6, 7);*

### Problem Limits

 Language Time Limit (seconds) C 0.50 C++ 0.50 C++14 0.01 C# 1.00 Go 1.00 Java 1.00 JavaScript 1.00 Objective-C 1.00 Perl 1.00 PHP 1.00 Python 1.00 Python3 1.00 Ruby 1.00 VB.Net 1.00

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