Problem: 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 (a_i)/(2) as possible. It means that either b_i = ⌊ (a_i)/(2) ⌋ or b_i = ⌈ (a_i)/(2) ⌉. In particular, if a_i is even, b_i = (a_i)/(2). Here ⌊ x ⌋ denotes rounding down to the largest integer not greater than x, and ⌈ x ⌉ 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 ≤ n ≤ 13 845), denoting the number of participants.

Each of the next n lines contains a single integer a_i (-336 ≤ a_i ≤ 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 = ⌊ (a_i)/(2) ⌋ or b_i = ⌈ (a_i)/(2) ⌉. 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.

Solution (in JAVA):

Solution:


import java.util.Scanner;

public class BalancedRating {
    public static void main(String[] args) {


        Scanner input = new Scanner(System.in);
        int n = input.nextInt();

        int[] unchangedRatings = new int[n];
        int[] ratings = new int[n];
        int neededNumber = 0;


        for (int i = 0; i < n; i++) {

            int userInput = input.nextInt();
            unchangedRatings[i] = userInput;
            ratings[i] = (userInput / 2);
            neededNumber += ratings[i];

        }

        if (neededNumber != 0) {

            for (int i = 0; i < ratings.length; i++) {


                if (Math.abs(unchangedRatings[i] % 2) == 1) {


                    if (neededNumber < 0) {
                        if (unchangedRatings[i] >= 0) {
                            ratings[i]++;//flooring
                            neededNumber++;
                        }
                    } else {
                        if (unchangedRatings[i] <= 0) {
                            ratings[i]--;//flooring
                            neededNumber--;
                        }
                    }

                    if (neededNumber == 0) {
                        break;
                    }
                }
            }
        }


        for (int element : ratings) {
            System.out.println(element);
        }


    }
}