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.util.*;

import java.io.*;

public class Cp {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] readline = br.readLine().split(" ");
		int n = Integer.parseInt(readline[0]);
		int data[] = new int[n];
		double carry = 0;
		for (int i = 0; i < data.length; i++) {
			data[i] = Integer.parseInt(br.readLine());
			if (data[i] % 2 == 0) {
				System.out.println(data[i] / 2);
			} else {
				if(carry==0) {
					System.out.println((int)data[i]/2);
					carry=data[i]/2.0-(int)(data[i]/2);
				}else {

					System.out.println((int)(data[i]/2.0+carry));
					carry=0;
				}
			}
		}

	}
}

class Pair implements Comparator<Pair>, Comparable<Pair> {
	int key, value;

	@Override
	public String toString() {
		// TODO Auto-generated method stub
		return "key:" + key + " value: " + value;
	}

	public Pair(int i, int j) {
		key = i;
		value = j;

	}

	@Override
	public int compare(Pair o1, Pair o2) {
		// TODO Auto-generated method stub
		return o1.compareTo(o2);
	}

	@Override
	public int hashCode() {
		// TODO Auto-generated method stub
		return key;
	}

	@Override
	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		return this.key - o.key;
	}

}

class TCS implements Comparable<TCS>, Comparator<TCS> {
	long i1, i2;

	@Override
	public String toString() {
		// TODO Auto-generated method stub
		return "i1:" + i1 + "  i2:" + i2;
	}

	TCS(long i1, long i2) {
		this.i1 = i1;
		this.i2 = i2;
	}

	@Override
	public int compareTo(TCS o) {
		// TODO Auto-generated method stub
		return compare(this, o);
	}

	@Override
	public int compare(TCS o1, TCS o2) {
		// TODO Auto-generated method stub
		return (int) ((o1.i1 == o2.i1) ? o1.i2 - o2.i2 : o1.i1 - o2.i1);
	}

	@Override
	public int hashCode() {
		// TODO Auto-generated method stub
		return super.hashCode();
	}

	@Override
	public boolean equals(Object obj) {
		// TODO Auto-generated method stub
		return super.equals(obj);
	}

}