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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 

	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		FastReader s=new FastReader();
		int t=1;
		StringBuilder result=new StringBuilder();
// 		while(t!=0)
// 		{
			t--;
		    int n=s.nextInt();
		    int arr[]=new int[n];
		    int ans[]=new int[n];
		  //  String[] str=s.nextLine().trim().split("\\s+");
		    int flag=1;
		    for(int i=0;i<n;i++)
		    {
		       arr[i]=Integer.parseInt(s.nextLine());
		    }
		    for(int i=0;i<n;i++)
		    {
		      // System.out.println("flag"+flag+" "+arr[i]);
		       if(arr[i]%2==0)
		       {
		           ans[i]=arr[i]/2;
		       }
		       else
		       {
		           if(flag==1)
		           {
		               if(arr[i]>0)
		               ans[i]=arr[i]/2;
		               else
		               ans[i]=(arr[i]/2)-1;
		               
		               flag=0;
		           }
		           else
		           {
		               if(arr[i]>0)
		               ans[i]=(arr[i]/2)+1;
		               else
		               ans[i]=arr[i]/2;
		               
		               flag=1;
		               
		           }
		       }
		    }
		  //}
		    for(int i=0;i<n;i++)
		    {
		        System.out.println(ans[i]);
		    }
		}
	
	}