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 div499{
static int mod = (int)1e8;
	public static void main(String sp[])throws IOException{
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		ArrayList<Long> al = new ArrayList<>();
		ArrayList<Long> al1 = new ArrayList<>();

		for(int i=0;i<n;i++) {
			al.add(sc.nextLong());
			al1.add(al.get(i));
		}
		
		long h1=0;
		long h2=0;
		for(int i=0;i<n;i++) {
			if(al.get(i)%2==0 && al.get(i)>=0) {
				h2+=al.get(i)/2;
				al.set(i, al.get(i)/2);
			}
			else if(al.get(i)%2==0 && al.get(i)<0) {
				h1+=al.get(i)/2;
				al.set(i, al.get(i)/2);
				
			}else {
				if(al.get(i)>=0)
					h2+=al.get(i)/2;
				else h1+=al.get(i)/2;
				al.set(i, al.get(i)/2);
			}
		}
		h1*=-1;
		for(int i=0;i<n;i++) {
			if(h1<h2 && al1.get(i)%2!=0 && al1.get(i)<0) {
				al.set(i, al.get(i)-1);
				h1+=1;
			}else if(h2<h1 &&al1.get(i)%2!=0 && al1.get(i)>=0){
				al.set(i, al.get(i)+1);
				h2+=1;
			}

		}
		for(int i=0;i<n;i++) {
			System.out.println(al.get(i));
		}
		
		
		
		
	}
public static long gcd(long a, long b){
	if(a==0)
		return b;
	
	return gcd(b%a,a);
}

public static void print(int[] arr){
	for(int i=0;i<arr.length;i++)
		System.out.print(arr[i]+" ");
	System.out.println();
}


public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
	
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
}