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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

import java.util.IdentityHashMap;
			
			
/**
 * for competitive programming
 * @author BrolyCode
 * @version 1.0.0
 */
			
			public class CP {
				static Random random;
				private static void mySort(int[] s) {
			        for (int i = 0; i < s.length; ++i) {
			            int j = random.nextInt(i + 1);
			            int t = s[i];
			            s[i] = s[j];
			            s[j] = t;
			        }
			        Arrays.sort(s);
			    }
				
				static class Pair{
					int x;
					int y;
					
					public Pair(int x, int y) {
						this.x=x;
						this.y=y;
					}
				}
				
				public static void sortPairX(Pair[] p) {
					Arrays.sort(p, new Comparator<Pair>() {
						public int compare(Pair o1, Pair o2) {
							return o1.x-o2.x;
						}			
					});
				}
				
				public static void sortPairY(Pair[] p) {
					Arrays.sort(p, new Comparator<Pair>() {
						public int compare(Pair o1, Pair o2) {
							return o1.y-o2.y;
						}			
					});
				}
				
				
			
				public static void main(String[] args) {
					random = new Random(543534151132L + System.currentTimeMillis());
					InputStream inputStream = System.in;
			        OutputStream outputStream = System.out;
			        InputReader in = new InputReader(inputStream);
			        PrintWriter out = new PrintWriter(outputStream);
			        
			        task(in,out);
			        
					out.close();
					
				}
				
			
				private static void task(InputReader in, PrintWriter out) {
					int n=in.nextInt();
					int rest=0;
					for(int i=0;i<n;i++) {
						int x=in.nextInt();
						if(Math.abs(x)%2==1) {
							if(x<0 && rest>=0) {
								rest--;
							}else if(x<0) {
								rest++;
								x--;
							}else if(x>0 && rest>=0) {
								rest--;
								x++;
							}else if(x>0) {
								rest++;
							}
						}
						out.println(x/2);
					}
				}

				public static int gcd(int a, int b)  
			    { 
			        BigInteger b1 = BigInteger.valueOf(a); 
			        BigInteger b2 = BigInteger.valueOf(b); 
			        BigInteger gcd = b1.gcd(b2); 
			            return gcd.intValue(); 
			    } 
			      
			    public static long gcd(long a, long b)  
			    { 
			        BigInteger b1 = BigInteger.valueOf(a); 
			        BigInteger b2 = BigInteger.valueOf(b); 
			        BigInteger gcd = b1.gcd(b2); 
			            return gcd.longValue(); 
			    } 
				
				static class InputReader {
			        public BufferedReader reader;
			        public StringTokenizer tokenizer;
			
			        public InputReader(InputStream stream) {
			            reader = new BufferedReader(new InputStreamReader(stream), 32768);
			            tokenizer = null;
			        }
			
			        public String next() {
			            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			                try {
			                    tokenizer = new StringTokenizer(reader.readLine());
			                } catch (IOException e) {
			                    throw new RuntimeException(e);
			                }
			            }
			            return tokenizer.nextToken();
			        }
			
			        public int nextInt() {
			            return Integer.parseInt(next());
			        }
			        
			        public long nextLong() {
			            return Long.parseLong(next());
			        }
			        
			        public double nextDouble() {
			            return Double.parseDouble(next());
			        }
			        
			        public float nextFloat() {
			            return Float.parseFloat(next());
			        }
			        
			    }
			
			}