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.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.Vector;
						
 
						
						
						public class ForLooops {
							 static class FastReader 
							    { 
							        BufferedReader br; 
							        StringTokenizer st; 
							       				  
							        public FastReader() 
							        { 
							            br = new BufferedReader(new
							                     InputStreamReader(System.in)); 
							        } 
							       
							        String next() 
							        { 
							            while (st == null || !st.hasMoreTokens()) 
							            { 
							                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; 
							        }
						
									public Character charAt(int i) {
										// TODO Auto-generated method stub
										return null;
									} 
									public BigInteger nextBigInteger() {
										// TODO Auto-generated method stub
										return null;
									} 
							    }
						
//							 static int gcd(int a , int b) {
//								 if(b==0)return a;
//								 return gcd(b,a%b);
//							 }
//						
//							
//							 static int m =(int) (1e9+7);
//							 static long mod(long x) {
//								 
//								 return ((x%m+m)%m);
//							 }
//							 static long add(long x,long y) {
//								 return mod((mod(x)+mod(y)));
//							 }
//							 static long mul(long x,long y) {
//								 return mod((mod(x)*mod(y)));
//							 }
							       
							public static void main(String[] args)throws IOException  {
								FastReader s=new FastReader();
								int t =s.nextInt();
								int sum=0;
								int flag=1;
								while(t-->0) {
									int n = s.nextInt();
									
									if(n%2==0) {
										n/=2;
										System.out.println(n);
									}
									else {
										System.out.println((n+flag)/2);
										flag*=-1;
									}
									
								}
								
								
							}
}