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.*;
import java.io.*;
public class Main {
    public static int log(int x){
        int c =0;
        while(x>0){
            x/=2;
            c++;
        }
        c--;
        return c;
    }
    static int pow(int a, int b){
        int l =1;
        for(int i=0; i<b; i++){
            l*=a;
        }
        return l;
    }
     static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
     static int lcm(int a, int b) 
    { 
        return (a*b)/gcd(a, b); 
    }
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
     	// String s = br.readLine();
        // char[] arr=s.toCharArray();
        // ArrayList<Integer> arrl = new ArrayList<Integer>(); 
        // TreeSet<Integer> ts1 = new TreeSet<Integer>(); 
        // HashSet<Integer> h = new HashSet<Integer>(); 
        // HashMap<Integer, Integer> map= new HashMap<>(); 
        // PriorityQueue<String> pQueue = new PriorityQueue<String>(); 
        // LinkedList<String> object = new LinkedList<String>(); 
        // StringBuilder str = new StringBuilder(); 
        
        
 	    StringTokenizer st = new StringTokenizer(br.readLine());
 	    	    int q = Integer.parseInt(st.nextToken());
 	    	    boolean fp=true;
 	    	    boolean fn = true;
        while(q-->0){
            st = new StringTokenizer(br.readLine());
         int n =Integer.parseInt(st.nextToken());
         if(n%2==0)                         System.out.println(n/2);
         else {
             if(n>0) {
                 if(fp)
               System.out.println(n/2);
               else                System.out.println(n/2+1);
                 fp=!fp;
             }else{
               if(fn)
               System.out.println(n/2);
               else                System.out.println(n/2-1);
                 fn=!fn;
             }
         }
        //  int[] arr = new int[n];
        //  for(int i=0; i<n; i++){
        //      arr[i] = Integer.parseInt(st.nextToken());
        //  }
 
         }
	}
}