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.util.*;

public class TestClass {
    public static void main(String args[] ) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Scanner sc = new Scanner(System.in);
        //String line = br.readLine();
        int n = sc.nextInt();
        int cc=0;
        int fc=0;
        int prev_idx=-1;
        int[] arr = new int[n];
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            //line = br.readLine();
            int val = sc.nextInt();
            arr[i] = val;
           //  System.out.println("hello "+val);
            if(val%2==0){
                ans[i] = val/2;
            }else{
                
                if(prev_idx==-1){
                    prev_idx = i;
                }else{
                   
                    int prev_sum = arr[i] + arr[prev_idx];
                    prev_sum = prev_sum/2;
                     
                    int val1 = arr[i]/2;
                    int val2 = arr[prev_idx]/2;
                    if(arr[i]<0 && arr[prev_idx]<0){
                        val1--;
                    }else if(arr[i]<0 && arr[prev_idx]>0){
                        
                    }else if(arr[prev_idx]<0 && arr[i]>0){
                        
                    }else{
                        val1++;
                    }
                    ans[i]=val1;
                    ans[prev_idx]= val2;
                    prev_idx=-1;
 
                }
            }
        }
        for (int i = 0; i < n; i++) {
            System.out.println(ans[i]);
        }
        
        
    }
}