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.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Solution {

    private static PrintWriter out;

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner(){
            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();
        }

        String nextLine() {
            String result = "";

            try {
                result = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return result;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        float nextFloat(){
            return Float.parseFloat(next());
        }

        long nextLong(){
            return Long.parseLong(next());
        }
    }

    public static void main(String args[]) {
        MyScanner scan = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        int n = scan.nextInt();

        int start[] = new int[n];
        for(int i = 0; i < n; i++){
            start[i] = scan.nextInt();
        }

        int result[] = numberFine(n, start);

        for(int i = 0; i < n; i++){
            out.println(result[i]);
        }

        out.close();
    }

    static int[] numberFine(int n, int start[]) {
        int arr[] = new int[n];

        int total = 0;
        for(int i = 0; i < n; i++){
            arr[i] = start[i]/2;
            total += arr[i];
        }

        if(total == 0) {
            return arr;
        }

        if(total > 0) {
            for(int i = 0; i < n; i++){
                if(arr[i] < 0 && start[i] % 2 != 0) {
                    arr[i]--;
                    total--;
                } else if(start[i] == -1) {
                    arr[i] = -1;
                    total--;
                }

//                if(arr[i] < 0 && start[i] % 2 != 0) {
//                    arr[i]--;
//                    total--;
//                }

                if(total == 0) {
                    break;
                }
            }
        } else {
            for(int i = 0; i < n; i++){
                if(arr[i] > 0 && start[i] % 2 != 0) {
                    arr[i]++;
                    total++;
                } else if(start[i] == 1) {
                    arr[i] = 1;
                    total++;
                }

//                if(arr[i] > 0 && start[i] % 2 != 0) {
//                    arr[i]++;
//                    total--;
//                }

                if(total == 0) {
                    break;
                }
            }
        }

        return arr;
    }
}