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;

/**
 *
 * @author imac
 */
public class NewMain2 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner s = new Scanner(System.in);
        int x = s.nextInt();
        int count_half_pos = 0;
        int count_half_neg = 0;

        int[] ar = new int[x];
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < ar.length; i++) {
            ar[i] = s.nextInt();
            if (Math.abs(ar[i]) % 2 == 1) {

                if (ar[i] > 0) {
                    count_half_pos++;
                } else {
                    count_half_neg++;
                }

                if (ar[i] < min) {
                    min = ar[i];
                }
            }
        }
        //System.out.println("count half " + count_half);
        //count_half = (int)(count_half * 0.5);

        count_half_neg /= 2;
        count_half_pos /= 2;

        //int sum = 0;
        for (int i = 0; i < x; i++) {

            if (Math.abs(ar[i]) % 2 == 1 && ar[i] > 0 && count_half_pos > 0) {
                ar[i] = (int) Math.ceil(ar[i] / 2.0);
                count_half_pos--;
            } else if (Math.abs(ar[i]) % 2 == 1 && ar[i] < 0 && count_half_neg > 0) {
                ar[i] = (int) Math.floor(ar[i] / 2.0);
                count_half_neg--;
            } else {
                ar[i] = ar[i] / 2;
            }

           // sum += ar[i];
            System.out.println(ar[i]);

        }
        //System.out.println("sum is " + sum);
    }

}