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A. Balanced Rating Changes

time limit per test

1 secondmemory limit per test

512 megabytesinput

standard inputoutput

standard outputAnother 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?

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.

Examples

Input

3 10 -5 -5

Output

5 -2 -3

Input

7 -7 -29 0 3 24 -29 38

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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