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.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;


public class A{
		
	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; 
        } 
    }
	

    private static int gcd(int a, int b) 
    { 
        if(a == 0) return b;
        if(b == 0) return a;
        return gcd(b,a%b); 
    } 
    
    public static void pal(int i,int j,String s)
    {	
    	int n = s.length();
    	while(i >= 0 && j < n)
    	{
    		if(s.charAt(i) == s.charAt(j))
    		{
    			psum[j] = Math.max(psum[j],i);
    		}
    		else
    		{
    			break;
    		}
    		i--;
    		j++;
    	}
    }
    
    static int psum[];
	public static void main(String[] args) throws IOException 
	{
		OutputStream outputStream = System.out;
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
        
        int n = sc.nextInt();
        boolean flag = true;
        while(n-- > 0)
        {
        	int x = sc.nextInt();
        	if(x%2 == 0)
        	{
        		out.println(x/2);
        	}
        	else
        	{
        		if(flag)
        		{
        			int y =0;
        			if(x < 0)
        			{
        				y = x/2;
        			}
        			else
        			{
        				y = x/2+1;
        			}
        			out.println(y);
        			flag = false;
        		}
        		else
        		{
        			int y = 0;
        			if(x < 0)
        			{
        				y = x/2-1;
        			}
        			else
        			{
        				y = x/2;
        			}
        			out.println(y);
        			flag = true;
        		}
        	}
        }
        out.close();
	}

}