CF1237A Balanced Rating Changes

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.