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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.PrintWriter;
import java.util.Arrays;




public class A {


	public static void main(String[]args)throws IOException {
		FastReader sc = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		int flag = 1;
		while (n-- > 0) {
			int a = sc.nextInt();
			if (a % 2 == 0) {
				out.println(a / 2);
			}

			else {
				out.println((a + flag) / 2);
				flag *= -1;
			}
		}

		out.close();
	}




// public static euclidTriplet euclidExtended(int a, int b) {
// 	if (b == 0)
// 		return new euclidTriplet(1, 0, a);

// 	euclidTriplet ans = euclidExtended(b, a % b);

// 	return new euclidTriplet(ans.y, ans.x - (a / b) * ans.y, ans.gcd);
// }


// public static int  gcd(int a, int b) {
// 	if (a == 0)
// 		return b;

// 	return gcd(b % a, a);
// }

}

// class euclidTriplet {
// 	int x, y, gcd;
// 	euclidTriplet(int x, int y, int gcd) {
// 		this.x = x;
// 		this.y = y;
// 		this.gcd = gcd;
// 	}
// }


// class comp implements Comparator<long []> {
// 	public int compare(long [] arr1, long[] arr2) {
// 		if ((2 * arr2[0] + arr2[1]) > (2 * arr1[0] + arr1[1]))
// 			return 1;

// 		else
// 			return -1;
// 	}
// }


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());
	}

	int [] nextIntArray(int n) {
		int [] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = nextInt();

		return arr;

	}


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

	long [] nextLongArray(int n) {
		long [] arr = new long[n];
		for (int i = 0; i < n; i++)
			arr[i] = nextLong();

		return arr;

	}

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

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

}