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 std::abs;
using std::array;
using std::cerr;
using std::cin;
using std::cout;
using std::generate;
using std::get;
using std::make_pair;
using std::make_tuple;
using std::map;
using std::max;
using std::max_element;
using std::min;
using std::min_element;
using std::pair;
using std::queue;
using std::reverse;
using std::set;
using std::sort;
using std::string;
using std::swap;
using std::tuple;
using std::unique;
using std::vector;
template <typename T>
T input() {
  T res;
  cin >> res;
  {};
  return res;
}
template <typename IT>
void input_seq(IT b, IT e) {
  std::generate(b, e,
                input<typename std::remove_reference<decltype(*b)>::type>);
}
int main() {
  std::iostream::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n = input<int>();
  int cr = 0;
  for (int i = 0; i < n; ++i) {
    int a = input<int>();
    int half = a / 2;
    if (a % 2 < 0) --half;
    if (2 * half != a) {
      if (cr == 1) ++half;
      cr ^= 1;
    }
    cout << half << "\n";
  }
  return 0;
}