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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package Contests;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 *
 * @author Akhilesh
 */
public class A1237 {
    public static void main(String[] args) throws IOException{
        BufferedReader scan = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(scan.readLine().trim());
        long sumNeg = 0, sumPos = 0;
        int check[] = new int[n];
        int arr[] = new int[n];
        for(int i = 0; i < n; i++){
            arr[i] = Integer.parseInt(scan.readLine().trim());
            check[i] = (int)(Math.abs(arr[i]))%2;
            if(arr[i] < 0){
                arr[i] = (int)(Math.floor(arr[i]/2.0));
                sumNeg += arr[i];
            }else
                if(arr[i] > 0){
                    arr[i] = (int)(Math.ceil(arr[i]/2.0));
                    sumPos += arr[i];
                }
        }
        long diff = sumPos + sumNeg;
        for(int i = 0; i < n; i++){
            if(check[i] == 1){
                if(diff > 0){
                    if(arr[i] > 0){
                        System.out.println(arr[i]-1);
                        diff--;
                    }else{
                        System.out.println(arr[i]);
                    }
                }else
                    if(diff < 0){
                        if(arr[i] < 0){
                            System.out.println(arr[i]+1);
                            diff++;
                        }else{
                            System.out.println(arr[i]);
                        }
                    }else{
                        System.out.println(arr[i]);
                    }
            }else{
                System.out.println(arr[i]);
            }
        }
    }
}