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.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.*;
import java.math.*;
import java.io.*;
import java.text.*;
import java.math.BigInteger;
 
public class Main
{  
 
    //Life's a bitch
    public static boolean[] sieve(long n)
    {
        boolean[] prime = new boolean[(int)n+1];
        Arrays.fill(prime,true);
        prime[0] = false;
        prime[1] = false;
        long m = (long)Math.sqrt(n);
        for(int i=2;i<=m;i++)
        {
            if(prime[i])
            {
                for(int k=i*i;k<=n;k+=i)
                {
                    prime[k] = false;
                }
            }
        }
        return prime;
    } 
 
    
    static long GCD(long a,long b)
    {
        if(b==0)
        {
            return a;
        }
        return GCD(b,a%b);
    }
 
    static long CountCoPrimes(long n)
    {
        long res = n;
        for(int i=2;i*i<=n;i++)
        {
            if(n%i==0)
            {
                while(n%i==0)
                {
                    n/=i;
                }
                res-=res/i;
            }
        }
        if(n>1)
        {
            res-=res/n;
        }
        return res;
    }
 
 
    
 
    
 
    static boolean prime(int n)
    {
        for(int i=2;i*i<=n;i++)
        {
            if(i%2==0 ||i%3==0)
            {
                return false;
            }
        }
        return true;
    }

    
 
   
 
 
   
   
  
    public static void main(String[] args) throws IOException
    {
     
        new Main().run();
       
    }
 
 	static void reverse(long[] a)
 	{	
 		int end = a.length-1;
 		int start = 0;
 		while(start<end)
 		{
 			long temp = a[start];
 			a[start] = a[end];
 			a[end] = temp;
 			start++;
 			end--;
 		}
 	}
   
 
    //chu
    // static int[] arr,tree[],lev;
    Scanner in = new Scanner(System.in);
    void run() throws IOException
    {
     	int flag = -1;
     	int q = ni();
     	while(q-->0)
     	{
     		int a = ni();
     		
     		if(a%2==0)
     		{
     			printL(a/2);
     		}
     		else
     		{
     			printL((a+flag)/2);
     			flag*=-1;

     		}

     	}
	}

	


	
	


   

 

    
 
 
 
 
 
 
    
 
    //xor range query
    static long xor(long n)
    {
 
        if(n%4==0)
        {
            return n;
        }
        if(n%4==1)
        {
            return  1;
        }
        if(n%4==2)
        {
            return n+1;
        }
        return 0;
    }
 
    static long xor(long a,long b)
    {
        return xor(b)^xor(a-1);
    }
 
 
    
 
  
   
    
 
    
       
    
 
    
   
  
 
 
 
   
 
     void printL(long a)
    {
        System.out.println(a);
    }
    void printS(String s)
    {
        System.out.println(s);
    }
 
     void printD(Double d)
    {
        System.out.println(d);
    }
  
   
   
    static void swap(char c,char p)
    {
        char t = c;
        c = p;
        p = t;
    }
 
    static long max(long n,long m)
    {
        return Math.max(n,m);
    }
    static long min(long n,long m)
    {
        return Math.min(n,m);
    }
 
    double nd() throws IOException
    {
        return Double.parseDouble(in.next());
    }
    int ni() throws IOException
    {
        return Integer.parseInt(in.next());
    }
 
    long nl() throws IOException
    {
        return Long.parseLong(in.next());
    }
 
    String si() throws IOException
    {
        return in.next();
    }
 
 
  
   
    static int abs(int n)
    {
        return Math.abs(n);
    }
 
    static class Scanner 
    {
        StringTokenizer st;
        BufferedReader br;
 
        public Scanner(InputStream s){  br = new BufferedReader(new InputStreamReader(s));}
 
        public String next() throws IOException 
        {
            while (st == null || !st.hasMoreTokens()) 
            {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }
 
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        
        public long nextLong() throws IOException {return Long.parseLong(next());}
 
        public String nextLine() throws IOException {return br.readLine();}
 
        public boolean ready() throws IOException {return br.ready();}
 
 
    }
 
    
}
 
 
 
class Pair implements Comparable<Pair>
{
   int x,y;
    public Pair(int x,int y)
    {
        this.x = x;
        this.y = y;
    }
    public int compareTo(Pair o)
    {
        return this.y-o.y;
    }
}