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 TipsAndHacks;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;


public class CC1 {
	static class Pair{
		int ty;
		int a;
		int b;
		Pair(int ty , int a , int b){
			this.ty = ty;
			this.a = a;
			this.b = b;
		}
	}
	static long mod = 1000000007;

	static long power(long x, long y) {
		long res = 1;

		while (y > 0) {
			if ((y & 1) != 0)
				res = (res * x) % mod;
			y = y >> 1;
			x = (x * x) % mod;
		}
		return res;
	}

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	public static void main(String[] args) {
		FastReader sc = new FastReader();
		int n = sc.nextInt();
		int a[] = new int [n];
		int odd = 0;
		for(int i = 0 ; i < n ; i++) {
			a[i] = sc.nextInt();
			if(a[i] % 2 != 0) {
				odd++;
			}
		}
		int up = odd / 2;
		int down = odd / 2;
		
		for(int i = 0 ; i < n; i++) {
			if(a[i] % 2 == 0) {
				System.out.println(a[i] / 2);
			}else {
				if(up > 0) {
					double za = (double)((double)a[i] / 2);
//					System.out.println(Math.ceil(-2.5));
//					System.out.println("lol");
					System.out.println((int)Math.ceil(za));
					up--;
				}else {
					double z = (double)((double)a[i] / 2);
//					System.out.println(z);
					System.out.println((int)Math.floor(z));
					down--;
				}
			}
		}
		
	}
}