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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Iterator;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main{
    public static void main(String[] args){
        FastReader sc=new FastReader();
        int n=sc.nextInt();
        int[] a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=sc.nextInt();
        }
        int flag=0;
        for(int i=0;i<n;i++){
            if(Math.abs(a[i])%2==0) System.out.println(a[i]/2);
            else if(flag==0) {
                System.out.println((a[i]+1)/2);flag=1;
            }
            else{
                System.out.println((a[i]-1)/2);flag=0;
            }
        }
    }
}

class FastReader{
    BufferedReader bf;
    StringTokenizer st;
    FastReader(){
        bf=new BufferedReader(new InputStreamReader(System.in));
    }
    
    public String next(){
        if(st==null || !st.hasMoreElements()){
            try{
                st=new StringTokenizer(bf.readLine());
            }catch(IOException e){
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    
    public long nextLong(){
        return Long.parseLong(next());
    }
    
    public int nextInt(){
        return Integer.parseInt(next());
    }
}