A. Balanced Rating Changes
implementation; math
Another Codeforces Round has just finished! It has gathered \(n\) participants, and according to the results, the expected rating change of participant \(i\) is \(a_i\). These rating changes are perfectly balanced — their sum is equal to \(0\).Unfortunately, due to minor technical glitches, the round is declared semi-rated. It means that all rating changes must be divided by two.There are two conditions though: For each participant \(i\), their modified rating change \(b_i\) must be integer, and as close to \(\frac{a_i}{2}\) as possible. It means that either \(b_i = \lfloor \frac{a_i}{2} \rfloor\) or \(b_i = \lceil \frac{a_i}{2} \rceil\). In particular, if \(a_i\) is even, \(b_i = \frac{a_i}{2}\). Here \(\lfloor x \rfloor\) denotes rounding down to the largest integer not greater than \(x\), and \(\lceil x \rceil\) denotes rounding up to the smallest integer not smaller than \(x\). The modified rating changes must be perfectly balanced — their sum must be equal to \(0\). Can you help with that?
The first line contains a single integer \(n\) (\(2 \le n \le 13\,845\)), denoting the number of participants.Each of the next \(n\) lines contains a single integer \(a_i\) (\(-336 \le a_i \le 1164\)), denoting the rating change of the \(i\)-th participant.The sum of all \(a_i\) is equal to \(0\).
Output \(n\) integers \(b_i\), each denoting the modified rating change of the \(i\)-th participant in order of input.For any \(i\), it must be true that either \(b_i = \lfloor \frac{a_i}{2} \rfloor\) or \(b_i = \lceil \frac{a_i}{2} \rceil\). The sum of all \(b_i\) must be equal to \(0\).If there are multiple solutions, print any. We can show that a solution exists for any valid input.
In the first example, \(b_1 = 5\), \(b_2 = -3\) and \(b_3 = -2\) is another correct solution.In the second example there are \(6\) possible solutions, one of them is shown in the example output.