Balanced Rating Changes

Description:

Input:

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:

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.

Sample Input:

3
10
-5
-5

Sample Output:

5
-2
-3

Sample Input:

7
-7
-29
0
3
24
-29
38

Sample Output:

-3
-15
0
2
12
-15
19

Note:

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.