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 javax.print.attribute.IntegerSyntax;
import java.io.*;
import java.util.*;

/**
 * A simple template for competitive programming problems.
 */
public class Banana {
    final InputReader in = new InputReader(System.in);
    final PrintWriter out = new PrintWriter(System.out);

    final long mod = 1000000009;


    void solve() {
        int a = -5;
        int n = in.nextInt();
        int[] arr = in.nextArray(n);

        boolean floor = true;
        for(int i=0; i<n; i++) {
            int fl = arr[i]/2;
            if(((arr[i]%2)+2)%2==1) {
                if(floor) {
                    out.println(arr[i]<0 ? fl-1 : fl);
                } else {
                    out.println(arr[i]<0 ? fl : fl+1);
                }
                floor = !floor;
            } else {
                out.println(fl);
            }
        }
    }

    public static void main(String[] args) throws FileNotFoundException { Banana s = new Banana(); s.solve(); s.out.close(); }

    public Banana() throws FileNotFoundException { }

    private static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        InputReader(InputStream stream) {
            this.stream = stream;
        }

        InputReader(String fileName) {
            InputStream stream = null;
            try {
                stream = new FileInputStream(fileName);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            this.stream = stream;
        }

        int[] nextArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }

        int[][] nextMatrix(int n, int m) {
            int[][] matrix = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    matrix[i][j] = nextInt();
            return matrix;
        }

        String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        double nextDouble() {
            return Double.parseDouble(nextString());
        }

        private int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try { numChars = stream.read(buf); }
                catch (IOException e) { throw new InputMismatchException(); }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        private boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }

        private boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
    }


}