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.*; 
import java.util.StringTokenizer; 
import java.io.PrintWriter;
import java.io.*;
import java.lang.*;
public class Ideone
{ 
    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 class aksh{
 
    int p;
    int q;
 
    public aksh(int a, int b) {
        p = a;
        q = b;
    }
    /*public int compareTo(aksh o)
    {
    return q-o.q; //ascending
    }*/
}
static long power(long x,long y) 
{ 
    long res = 1;      // Initialize result 
  
      // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y%2==1) 
            res = (res*x); 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x);   
    } 
    return res; 
} 
 
 static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
  static int findGCD(int arr[], int n) 
    { 
        int result = arr[0]; 
        for (int i = 1; i < n; i++) 
            result = gcd(arr[i], result); 
  
        return result; 
    } 
 
    static class edge implements Comparable<edge>
     {
            int to;
            long weight;
            
            public edge(int a, long b) 
            {
                to = a;
                weight = b;
            }
            public int compareTo(edge o) 
            {
                return Long.compare(weight, o.weight);
            }
     }
    
    static ArrayList<edge>[] adj;
    static int[] vis;
/*    static void dfs(int x)
    {
        vis[x] = 1;
 
     for (int v : adj[x])
     {
        if (vis[v]==0)
        dfs(v);
     }
    }*/
 
    /*static void dfs(int v, int d) //modified for finding levels
    {
            c[v] = (d + 1);
            vis[v] = 1;
            for (int e : adj[v])
            {
                if (vis[e]==0) 
                {
                    dfs(e, d ^ 1);
                }
            }
    }*/
 
    /*static boolean dfs(int i)
    {
        for(int j:adj[i])
        {
            if(vis[j]==-1)
            {
                vis[j]=i;
                if(dfs(j))
                    return true;
            }
 
            else if(j!=vis[i])
            {
                res[cnt++]=j;
                while(j!=i)
                {
                    res[cnt++]=i;
                    i=vis[i];
                }
                res[cnt++]=j;
                return true;
            }
        }
 
        return false;
    }*/
 
 
   static final long INF = Long.MAX_VALUE/5;
    public static void main(String args[] ) throws Exception 
    {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT */
         FastReader sc=new FastReader();
         int n=sc.nextInt();
         int[] a=new int[n];

         for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
         boolean flag=true;

         for(int i=0;i<n;i++)
         {
            if((Math.abs(a[i]))%2==1)
            {
                 if(a[i]<0)
                 {
                    if(flag==true)
                    {
                        a[i]=(int)Math.floor((double)a[i]/2);
                        flag=!flag;   
                    }
                    else
                    {
                          a[i]=(int)Math.ceil((double)a[i]/2);
                          flag=!flag;
                    }
              
                 }
                 else
                 {
                    if(flag)
                    {
                        a[i]=(int)Math.floor((double)a[i]/2);
                        flag=!flag;
                    }
                    else
                    {
                        a[i]=(int)Math.ceil((double)a[i]/2);
                        flag=!flag;
                    }
                 }
             }

                  else
                  a[i]=a[i]/2;
           }


           for(int i=0;i<n;i++)
            System.out.println(a[i]);
         

 
    }
}