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.io.File;
import java.util.Scanner;
import java.util.ArrayList;

public class BalancedRatingChanges {
    public static void main(String [] args) throws Exception
    {
        Scanner sc = new Scanner(System.in);

        int numCases = Integer.parseInt(sc.nextLine());


        ArrayList<object> finalAll = new ArrayList<>();

        int totalPos = 0;
        int totalNeg = 0;
        int counter = 0;


        for(int x=0;x<numCases;x++)
        {
            int num = Integer.parseInt(sc.nextLine());

            finalAll.add(new object(num/2, num,counter));


            counter++;
        }


        for(int x=0;x<finalAll.size();x++)
        {
            if(finalAll.get(x).getVal()>=0)
            {
                totalPos += finalAll.get(x).getVal();
            }
            if(finalAll.get(x).getVal()<0)
            {
                totalNeg += finalAll.get(x).getVal();
            }
        }
        if(totalPos+totalNeg == 0)
        {
            for(int x=0;x<finalAll.size();x++)
                System.out.println(finalAll.get(x).getVal());
        }
        else
        {


                for(int x=0; x<finalAll.size();x++)
                {
                    if(finalAll.get(x).getOldVal()%2==1 && finalAll.get(x).getOldVal()%2>=0)
                    {
                        totalPos ++;
                        finalAll.get(x).setVal(finalAll.get(x).getVal()+1);

                    }
                    if(Math.abs(finalAll.get(x).getOldVal())%2==1 && finalAll.get(x).getOldVal()%2<0)
                    {
                        totalNeg --;
                        finalAll.get(x).setVal(finalAll.get(x).getVal()-1);

                    }
                    if(totalPos+totalNeg==0)
                        break;


                }

            for(int x=0;x<finalAll.size();x++)
                System.out.println(finalAll.get(x).getVal());
        }



    }
    public static class object
    {
        int oldVal;
        int val;
        int id;

        object(int val,  int oldVal, int id)
        {
            this.oldVal = oldVal;
            this.val = val;
            this.id = id;
        }

        public int getVal() {
            return val;
        }

        public void setVal(int val) {
            this.val = val;
        }

        public int getId() {
            return id;
        }

        public void setId(int id) {
            this.id = id;
        }

        public int getOldVal() {
            return oldVal;
        }

        public void setOldVal(int oldVal) {
            this.oldVal = oldVal;
        }
    }
}