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.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
public class test
{   
static 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()); 		
} 
		
long nextLong() 		
{ 			
return Long.parseLong(next()); 		
} 
		
double nextDouble() 		
{ 			
return Double.parseDouble(next()); 		
		 } 
		
		String nextLine() 		
		 { 			
String str = ""; 			
			 try			
			{ 				
				 str = br.readLine(); 			
			 } 			
			 catch (IOException e) 			
			 { 				
				 e.printStackTrace(); 			
			 } 			
			 return str; 		
		 } 	
	 }
	//~ static int bigger(int target){
		//~ int ans = -1;
		//~ int left = 0;
		//~ int right = n-1;
		//~ while(left <= right){
		//~ int mid = left  + (right - left)/2;
		//~ if(arr[mid]>target){
		//~ ans = arr[mid];
		//~ right = mid -1;	
		//~ }else{
		//~ left = mid + 1;	
		//~ }
		//~ }
		//~ return ans;
	//~ }
	
	
	//~ static int lower(int target){
		//~ int ans = -1;
		//~ int left = 0;
		//~ int right = n-1;
		//~ while(left <= right){
		//~ int mid = left + (right - left )/2;
		//~ if(arr[mid] <target){
		//~ ans = arr[mid];
		//~ left = mid+1;	
			
		//~ }else{
			
		//~ right = mid-1;
		//~ }	
			
		//~ }
		//~ return ans;
	//~ }
	
	
	 public static void main(String[] args){
		 FastReader scan=new FastReader();
		int n = scan.nextInt();
		int[] arr = new int[n];
		for(int i=0;i<n;i++)arr[i] = scan.nextInt();
		int[] ans = new int[n];
		int sum = 0;
		for(int i=0;i<n;i++){
			sum += arr[i]/2;
			ans[i] = arr[i]/2;
		}
		//~ System.out.println("sum ---- " + sum);
		if(sum == 0){
			for(int i=0;i<n;i++){
			System.out.println(ans[i]);	
			}
			
		}else if(sum >0){
			for(int i=0;i<n;i++){
			if(sum !=0 && arr[i] < 0 && arr[i]%2 !=0){
			ans[i] = (arr[i]/2) - 1;	
			sum--;
			}	
				
			}
			for(int i=0;i<n;i++){
			System.out.println(ans[i]);	
				
			}
		}else{
			for(int i=0;i<n;i++){
			if(sum != 0 && arr[i] >0 && arr[i]%2 !=0){
				ans[i] = (arr[i]/2) + 1;
				sum++;	
			}	
				
				
			}
			for(int i=0;i<n;i++){
			System.out.println(ans[i]);	
				
			}
				
			
		}
		 
			
		}
	}