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.*;
import java.util.*;

public class A {
    public static void main(String args[]) {
        FastScanner scn = new FastScanner();
        int n = scn.nextInt();
        int a[] = new int[n];
        int b[] = new int[n];
        int sum = 0;
        for (int i = 0; i < n; ++i) {
            a[i] = scn.nextInt();
            b[i] = a[i] / 2;
            sum += b[i];
        }
        if (sum == 0) {
            for (int i = 0; i < n; ++i) {
                System.out.println(b[i]);
            }
        } else if (sum > 0) {
            for (int i = 0; i < n && sum > 0; ++i) {
                if (a[i] < 0 && a[i] % 2 != 0) {
                    b[i] -= 1;
                    sum--;
                }
            }
            if (sum > 0) {
                for (int i = 0; i < n && sum > 0; ++i) {
                    if (a[i] < 0) {
                        b[i] -= 1;
                        sum--;
                    }
                }
            }
            for (int i = 0; i < n; ++i) {
                System.out.println(b[i]);
            }
        } else {
            for (int i = 0; i < n && sum < 0; ++i) {
                if (a[i] > 0 && a[i] % 2 != 0) {
                    b[i] += 1;
                    sum++;
                }
            }
            if (sum < 0) {
                for (int i = 0; i < n && sum < 0; ++i) {
                    if (a[i] > 0) {
                        b[i] += 1;
                        sum++;
                    }
                }
            }
            for (int i = 0; i < n; ++i) {
                System.out.println(b[i]);
            }
        }


    }

    public static int bin(ArrayList<Integer> ar, int target) {
        int h = ar.size() - 1;
        int l = 0;
        int ans = -1;
        while (l < h) {
            int m = l + (h - l) / 2;
            if (ar.get(m) > target) {
                h = m - 1;
            } else {
                l = m;
                ans = m;
            }
        }
        return ans;
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

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