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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool isprime(int n) {
  if (n == 1) return false;
  if (n == 2) return true;
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
void answer(int f) {
  if (f) {
    cout << "YES";
  } else {
    cout << "NO";
  }
  cout << endl;
}
long long int solve(long long int n, long long int i, long long int ans) {
  if (n == 0) return ans;
  if (n % 3 == 0)
    solve((n / 3) - 1, i + 1, ans);
  else if (i > 0)
    solve(n - 1, i - 1, ans + 1);
  else
    return -1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  int t = 1;
  while (t--) {
    long long int n;
    cin >> n;
    int a[n];
    int f = 0;
    long long int i;
    long long int x = 0;
    for (i = 0; i < n; i++) {
      cin >> a[i];
      if (a[i] % 2 == 0)
        cout << a[i] / 2;
      else {
        if (a[i] < 0) {
          cout << (a[i] / 2) - f;
          f = (f + 1) % 2;
        } else {
          cout << (a[i] / 2) + x;
          x = (x + 1) % 2;
        }
      }
      cout << endl;
    }
  }
}