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:
/******************************************************************************

                            Online Java Compiler.
                Code, Compile, Run and Debug java program online.
Write your code in this editor and press "Run" button to execute it.

*******************************************************************************/
import java.util.Scanner;
import java.util.*;

public class Main
{
  public static int[] balancedRatingChanges (int[]participants,
					     int number_participants)
  {
    int result[] = new int[number_participants];
    int fin = 0;
    double value = 0;
    int mod = 0;
    int divsor = 1;
    for (int i = 0; i < number_participants; i++)
      {
	if (participants[i] == 0)
	  {
	    result[i] = 0;
	  }
	else
	  {
	    value = participants[i] / 2.0;
	    mod = participants[i] % 2;
	    if (mod == 0)
	      {
		result[i] = (int) value;
	      }
	    else
	      {
		if (divsor % 2 == 0)
		  {
		    result[i] = (int) Math.floor (value);
		  }
		else
		  {
		    result[i] = (int) Math.ceil (value);
		  }
		divsor++;
	      }
	  }
	fin += result[i];

      }
    return result;
  }
  public static void main (String[]args)
  {
    Scanner sc = new Scanner (System.in);
    int num = sc.nextInt ();
    int arr[] = new int[num];

    for (int j = 0; j < num; j++)
      {
	int val = sc.nextInt ();
	arr[j] = val;
      }

    int[] result = balancedRatingChanges (arr, num);
    for (int j = 0; j < result.length; j++)
      {
	System.out.println (result[j]);
      }

  }
}