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 com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class AP1 {
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int n=scan.nextInt();
        int[] arr=new int[n];
        int[] mod=new int[n];
        long sum=0;
        for(int i=0;i<n;i++){
            arr[i]=scan.nextInt();
            sum+=arr[i]/2;
            if(arr[i]%2==0){
                mod[i]=1;
                arr[i]/=2;
            }
        }
        int i=0;
        while(sum!=0&&i<n){
            if(sum<0){
                if(mod[i]==0){
                    if(arr[i]<0){
                        arr[i]=arr[i]/2;
                    }
                    else{
                        arr[i]=arr[i]/2+1;
                        sum++;
                    }
                }
            }
            else{
                if(mod[i]==0){
                    if(arr[i]<0){
                        arr[i]=arr[i]/2-1;
                        sum--;
                    }
                    else{
                        arr[i]=arr[i]/2;
                    }
                }
            }
            i++;
        }
        if(sum==0){
            for (; i <n ; i++) {
                if(mod[i]==0){
                    arr[i]/=2;
                }
            }
        }
        StringBuilder print=new StringBuilder();
        for(int j=0;j<n;j++){
            print.append(arr[j]+"\n");
        }
        System.out.println(print);
    }
    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;
        }
    }

}