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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class A {

	public static void main(String[] args) {
		FS in = new FS();
		PrintWriter out = new PrintWriter(System.out);
		
		int N = in.nextInt();
		int ar[] = new int[N];
		int sum = 0;
		boolean o[] = new boolean[N];
		for(int i = 0; i < N; i++) {
			ar[i] = in.nextInt();
			o[i] = Math.abs(ar[i])%2 == 1;
			ar[i] = ar[i] > 0 ? (ar[i]+1)/2 : (ar[i]-1)/2;
			sum += ar[i];
		}
		for(int i = 0; i < N; i++) {
			if(sum == 0) break;
			if(!o[i]) continue;
			if(ar[i] < 0) {
				if(sum < 0) { ar[i]++; sum++;}
			}
			else {
				if(sum > 0) { ar[i]--; sum--;}
			}
		}
		for(int ii : ar)out.println(ii);
		out.close();
	}

	static class FS{
		BufferedReader br;
		StringTokenizer st;
		public FS() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		public String next() {
			while(st == null || !st.hasMoreElements()) {
				try { st = new StringTokenizer(br.readLine());}
				catch(Exception e) { throw null;}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}