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.InputStreamReader;
import java.io.IOException;
import java.util.*;
import java.lang.Math;
 
public class Solution {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static long mod = 1000000000+7;
    
	public static void main(String[] args) throws IOException {
 	    // Read inputs
//  	    st = new StringTokenizer(br.readLine());
//  		int q = Integer.parseInt(st.nextToken());
//  		for(int i = 0; i<q; i++){
		    solve();
//  		}
	}
	
	public static void solve() throws IOException {
	    // Read inputs
	    st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
	    int[] a = new int[n];
	    
	    for(int i = 0; i<n; i++) {
	        st = new StringTokenizer(br.readLine());
	        a[i] = Integer.parseInt(st.nextToken());
	    }
	    
	    int oddAcc = 0;
	    
	    for(int i : a) {
	        if(i%2==0) System.out.println(i/2);
	        else {
	            int out = i/2;
	            if(i>0 && oddAcc>0) {
	                out = i/2 + 1;
	            } else if (i<0 && oddAcc<0) out = i/2 -1;
	            System.out.println(out);
	            oddAcc += i - 2*out;
	        }
	    }
	}
}