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:
//BalanceRatChanges
import java.io.*;
import java.util.*;
public class BalanceRatChanges{
static int t,n,h;
static int[] arr;
static StringBuilder ans=new StringBuilder();
public static void  solve(){
   boolean flag=true;
   for(int i=0;i<n;i++){
   	
   	  if((Math.abs(arr[i])%2)==1){
   	  	if(flag){
   	  		ans.append((int)Math.ceil((double)arr[i]/2)+"\n");
   	  		flag=false;
   	  	}
   	  	else{
   	  		ans.append((int)Math.floor((double)arr[i]/2)+"\n");
   	  		flag=true;
   	  	}
   	  }
   	  else{
   	  	ans.append((int)Math.ceil((double)arr[i]/2)+"\n");
   	  }
   }
}		
public static void main(String[] args) throws IOException{
		// BufferedReader br = new BufferedReader(new
  //      FileReader("sampleinp.txt"));
    	BufferedReader br = new BufferedReader( 
                             new InputStreamReader(System.in)); 
		
	 	n=Integer.parseInt(br.readLine());	 		
	 	arr=new int[n];	
	 	for(int i=0;i<n;i++){
	 		arr[i]=Integer.parseInt(br.readLine());
	 	}
	 	solve();				
	 	System.out.println(ans.toString());

    }
}