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.*;

public class Main {
    public static void main(String[] args) throws IOException {
int a = nI();
boolean pm = false;
boolean pp = false;
        for (int i = 0; i < a; i++) {
            int b = nI();
            if(b%2==0){
                out.println(b/2);
            }else{
             if(b<0){
                 if(pm){
                     out.println(b/2-1);
                     pm = false;
                 }else{
                     out.println(b/2);
                     pm = true;
                 }
             }else{
                     if (pp) {
                         out.println(b / 2 + 1);
                         pp = false;
                     } else {
                         out.println(b / 2);
                         pp = true;
                     }
             }
            }
        }
      out.close();
    }



























        static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static BufferedReader brfile;
    static PrintWriter outfile;
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer in = new StringTokenizer("");

    static {
        try {
            brfile = new BufferedReader(new FileReader(new File("input.txt")));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    static {
        try {
            outfile = new PrintWriter("output.txt");
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }


    public static String nT() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public static int nI() throws IOException {
        return Integer.parseInt(nT());
    }

    public static double nD() throws IOException {
        return Double.parseDouble(nT());
    }

    public static long nL() throws IOException {
        return Long.parseLong(nT());
    }
}