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 a {
	public static void main(String[] args) throws IOException {
        new a();
    }
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	
    int n, par = 0;
    int[] a, b;
	
	a() throws IOException {
		n = in.nextInt();
        int oddn, oddp;
        a = new int[n]; b = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            if (a[i] %2 == 0)
                b[i] = a[i]/2;
            else if (a[i] < 0) {
                b[i] = a[i]/2 + (par %2 == 0 ? -1 : 0);
                par++;
            }
            else {
                b[i] = a[i]/2 + (par %2 == 1 ? 1 : 0);
                par++;
            }
        }

        for (int bb : b)
            out.println(bb);

		out.close();	
	}
	
	class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream i) {
		    br = new BufferedReader(new InputStreamReader(i));
		    st = new StringTokenizer("");
		}		
		public String next() throws IOException {
		    if(st.hasMoreTokens())
		        return st.nextToken();
		    else
		        st = new StringTokenizer(br.readLine());
		    return next();
		}
		public int nextInt() throws IOException {
		    return Integer.parseInt(next());
		}
	    public long nextLong() throws IOException {
		    return Long.parseLong(next());
		}
		public double nextDouble() throws IOException {
		    return Double.parseDouble(next());
		}
    }
}