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.InputStreamReader;
import java.util.StringTokenizer; 
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.*;
public class solution
{ 
    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; 
        } 
    }
    static long gcd(long a,long b)
    {
    	if(b==0)
    		return a;
    	return gcd(b,a%b);
    }
   
    public static void main(String[] args)throws IOException
    {
        FastReader in=new FastReader();
        int t=1,i;
        while(t-->0)
        {
        	int n=in.nextInt();
        	int a[]=new int[n];
        	for(i=0;i<n;i++)
        		a[i]=in.nextInt();
        	int b=0,c=0,d=0,e=0;
        	for(i=0;i<n;i++)
        	{
        	if(a[i]%2==1)
        		c++;
        		else if(a[i]%2==-1)		
        			e++;
       	}
       	//System.out.println(c+" "+e);
        	int cnt=0,x=Math.abs(c-e);
        	x=x/2;
        	if(c>=e)
        	{
        		for(i=0;i<n;i++)
        		{
        			if(a[i]%2==0)
        				a[i]=a[i]/2;
        	else if(a[i]%2==-1)
        		a[i]=a[i]/2;
else if(a[i]%2==1)
{
	if(cnt<x)
	{
	a[i]=(a[i]/2)+1;
	cnt++;
	}
	else
		a[i]=a[i]/2;
}
}
}
else
{
	for(i=0;i<n;i++)
        		{
        			if(a[i]%2==0)
        				a[i]=a[i]/2;
        	else if(a[i]%2==1)
        		a[i]=a[i]/2;
else if(a[i]%2==-1)
{
	if(cnt<x)
	{
	a[i]=(a[i]/2)-1;
	cnt++;
	}
	else
		a[i]=a[i]/2;
}
}
}
for(i=0;i<n;i++)
	System.out.println(a[i]);
}
}
}