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.*;

public class Main {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);

    int N = in.nextInt();
    int[] original = new int[N];
    int[] answer = new int[N];
    int sum = 0;

    for (int i = 0; i < N; i++) {
      original[i] = in.nextInt();
      answer[i] = original[i] / 2;
      sum += answer[i];
    }

    if (sum > 0) {
      // Add -1 to answer[i] where original[i] < 0 && original[i] % 2 == 1
      for (int i = 0; i < N && sum > 0; i++) {
        if (original[i] < 0 && original[i] % 2 == -1) {
          answer[i]--;
          sum--;
        }
      }
    } else if (sum < 0) {
      // Add 1 to answer[i] where original[i] > 0 && original[i] % 2 == 1
      for (int i = 0; i < N && sum < 0; i++) {
        if (original[i] > 0 && original[i] % 2 == 1) {
          answer[i]++;
          sum++;
        }
      }
    }

    for (int i = 0; i < N; i++) {
      System.out.println(answer[i]);
    }
  }

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

  }

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

  public static void print(Object o) {
    System.out.println(o);
  }
}