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.*;
        import java.util.*;
        import java.lang.*;
             
            public class d {
            	public static void main (String[] args) {
            	PrintWriter pw=new PrintWriter(System.out);
            	Scanner sc=new Scanner(System.in);
            	
                
                int n=sc.nextInt();
                 int[] a=new int[n];
int[] b=new int[n];
              for(int i=0;i<n;i++){
        a[i]=sc.nextInt();
        b[i]=a[i];}
int c1=0,c2=0,sum=0;
             for(int i=0;i<n;i++){
   if(a[i]<0&&Math.abs(a[i])%2==1)
   a[i]=(a[i]/2)-1;
    else
     a[i]=a[i]/2;
}
for(int i=0;i<n;i++)
   sum+=a[i];


if(sum<0){
for(int i=0;i<n;i++){
   if(Math.abs(b[i])%2==1){
     a[i]++;
     sum++;}

    if(sum==0)
    break;}

}
for(int i=0;i<n;i++)
  pw.println(a[i]);
                pw.close();
            	}
            }