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 BalancedRatingchanges
{
    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long sumpos = 0l;
        long sumneg = 0l;
        int countpos = 0;
        int countneg = 0;
        int rank [] = new int[n];
        for(int  i = 0; i < n ; i++ )
        {
            rank[i] = sc.nextInt();

//            when ranking is positive nd not even
            if(rank[i]>0)
            {
//                System.out.println("pos");
                if(rank[i]%2!=0)
                    countpos++;
                sumpos += (rank[i]/2);
            }

//            when ranking is negative and not even
            else if(rank[i]<0)
            {
//                System.out.println("neg");
                if(rank[i]%2!=0)
                    countneg++;
                sumneg += (rank[i]/2);
            }
        }
//        System.out.println("sum pos "+sumpos);
//        System.out.println("sum neg "+sumneg);/

        if(sumpos+sumneg!=0)
        {
            if(sumpos+sumneg>0)
            {
//                System.out.println("here >0");
                long k = sumpos+sumneg;

                int c = 0;
                for(int i = 0;i < n;i++)
                {
                    if(rank[i]<0&&rank[i]%2!=0&&c<k)
                    {
                        System.out.println(((rank[i] / 2) - 1));
                    c++;
                    }
                    else
                        System.out.println(rank[i]/2);
                }



            }
            else if(sumpos+sumneg<0)
            {
//                System.out.println("here  <0");


                long k =Math.abs( sumpos+sumneg);

                int c = 0;
                for(int i = 0;i < n;i++)
                {
                    if(rank[i]>0&&rank[i]%2!=0&&c<k)
                    {
//                        System.out.println("pos change");
                        System.out.println(((rank[i] / 2) + 1));
                        c++;
                    }
                    else
                        System.out.println(rank[i]/2);
                }
            }



        }
        else
        {
//            System.out.println("here ==0");
            for(int i = 0; i < n;i++)
            {
                System.out.println(rank[i]/2);
            }
        }

    }
}