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 competitiveprogramming;

import java.io.*;
import java.util.*;

public class balancedratingchanges {
    public static void main(String[] args) throws IOException {
        FastScanner scan = new FastScanner();
        int n = scan.nextInt();
        int[] changes = new int[n];
        boolean[] isOdd = new boolean[n];
        int[] ori = new int[n];
        int sum = 0;
        for (int i = 0; i < n; i++) {
        	int c = scan.nextInt();
        	changes[i] = c/2;
        	ori[i] = c;
        	if (c % 2 == 1 || c % 2 == -1) {
        		isOdd[i] = true;
        	}
        	else {
        		isOdd[i] = false;
        	}
        	sum += c/2;
        }
        //System.out.println(Arrays.toString(isOdd));
        for (int i = 0; i < n; i++) {
        	//System.out.println(sum + " " + changes[i]);
        	if (sum == 0) {
        		break;
        	}
        	if (isOdd[i]) {
        		//System.out.println("asdkfjasdf");
        		if (sum < 0) {
        			if (ori[i] > 0) {
        				changes[i] += 1;
        				sum += 1;
        			}
        		}
        		else if (sum > 0) {
        			if (ori[i] < 0){
        				changes[i] -= 1;
        				sum -= 1;
        			}
        		}
        	}
        }
       // System.out.println(sum);
        
        for (int i = 0; i < n; i++) {
        	System.out.println(changes[i]);
        }
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return null;
        }

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

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

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}