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.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	    FastReader fr = new FastReader();
	    int n = fr.nextInt();
	    int[] a = new int[n];
	    int neg=0,pos=0;
	    for(int i=0;i<n;i++){
	        int x = fr.nextInt();
	        a[i] = x;
	        if(a[i]>0){
	            pos+=a[i]/2;
	        }else{
	            neg+=a[i]/2;
	        }
	    }
	    int i=0;
	    while(pos+neg!=0&&i<n){
	        int x = pos+neg;
	        if(x>0){
	            if(a[i]>0){
	                a[i] = a[i]/2;
	            }else{
	                double y = a[i]/2.0;
	                if(a[i]/2!=y){
	                    a[i] = a[i]/2-1;
	                    neg--;
	                }else{
	                    a[i] = a[i]/2;
	                }
	            }
	        }else{
	            if(a[i]<0){
	                a[i] = a[i]/2;
	            }else{
	                double y = a[i]/2.0;
	                if(a[i]/2!=y){
	                    a[i]=a[i]/2+1;
	                    pos++;
	                }else{
	                    a[i] = a[i]/2;
	                }
	            }
	        }
	        i++;
	    }
	    while(i<n){
	        a[i] = a[i]/2;
	        i++;
	    }
	    for(int j=0;j<n;j++){
	        if(j==n-1){
	            System.out.println(a[j]);
	        }else{
	            System.out.println(a[j]+" ");
	        }
	    }
	}
}
class FastReader {
 
    BufferedReader bf;
    StringTokenizer st;
 
    public FastReader() {
        bf = new BufferedReader(new InputStreamReader(System.in));
    }
 
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(bf.readLine());
            } catch (Exception e) {
                System.out.println(e);
            }
        }
        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 = bf.readLine();
        } catch (Exception e) {
            System.out.println(e);
        }
        return str;
    }
}