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.*;
import java.util.*;
import java.math.*;
     
public class Main {
	//static int dir[][]={{0,1},{0,-1},{1,0},{-1,0}};
	public static void main(String[] args) throws Exception {
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        OutputStream outputStream = System.out;
    	PrintWriter out = new PrintWriter(outputStream);
 
        int i, j;
		
		int n=Integer.parseInt(br.readLine());
		int[] ar = new int[n];
		int neg=0, pos=0;
		
		for(i=0;i<n;i++){
		    ar[i]=Integer.parseInt(br.readLine());
		    if(ar[i]<0 && ar[i]%2!=0)
		        neg++;
		    else
		    if(ar[i]>0 && ar[i]%2!=0)
		        pos++;
		}
		int m;
		if(neg%2==0)
		    m=0;
		else
		    m=1;
		
		int h=0;    
		for(i=0;i<n;i++)
		{
		    if(ar[i]<0 && ar[i]%2!=0)
            {
                if(h==0)
                    ar[i]=(int)Math.floor((double)ar[i]/2);
                else
                    ar[i]=(int)Math.ceil((double)ar[i]/2);
                h=1-h;
               // out.print(ar[i]+" ");
            }
		    else
		    if(ar[i]>0 && ar[i]%2!=0)
		    {
		        if(m==0)
                    ar[i]=(int)Math.floor((double)ar[i]/2);
                else
                    ar[i]=(int)Math.ceil((double)ar[i]/2);
                m=1-m;
		    }
		    else
		    if(ar[i]%2==0)
		    {
		        ar[i]=ar[i]/2;
		    }
		}
		
		for(i=0;i<n;i++)
		    out.println(ar[i]);
		out.flush();
    	out.close();
    	}
    }