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;
long long modd = 1000 * 1000 * 1000 + 7;
template <class T>
class depth_first_search_iterator {
 public:
  stack<pair<T, T>> todo;
  function<bool(T)> notvisited;
  function<void(T)> mark_visited;
  function<set<T>(T)> neighbors;
  depth_first_search_iterator() {}
  depth_first_search_iterator(T start, function<bool(T)> notv,
                              function<void(T)> mark_v,
                              function<set<T>(T)> neigh)
      : notvisited(notv),
        mark_visited(mark_v),
        neighbors(neigh),
        end_(false),
        current(start),
        prev(start) {
    todo.push(make_pair(start, start));
    operator++();
  }
  void operator++() {
    end_ = true;
    while (!todo.empty()) {
      current = todo.top().first;
      prev = todo.top().second;
      todo.pop();
      if (notvisited(current)) {
        mark_visited(current);
        for (const T x : neighbors(current)) {
          todo.push(make_pair(x, current));
        }
        end_ = false;
        break;
      }
    }
  }
  T operator*() { return current; }
  T previous() { return prev; }
  bool end() { return end_; }

 private:
  T current;
  T prev;
  bool end_;
};
template <class T>
class breadth_first_search_iterator {
 public:
  queue<pair<T, T>> todo;
  function<bool(T)> notvisited;
  function<void(T)> mark_visited;
  function<set<T>(T)> neighbors;
  breadth_first_search_iterator() {}
  breadth_first_search_iterator(T start, function<bool(T)> notv,
                                function<void(T)> mark_v,
                                function<set<T>(T)> neigh)
      : notvisited(notv),
        mark_visited(mark_v),
        neighbors(neigh),
        end_(false),
        current(start),
        prev(start) {
    todo.push(make_pair(start, start));
    operator++();
  }
  void operator++() {
    end_ = true;
    while (!todo.empty()) {
      current = todo.front().first;
      prev = todo.front().second;
      todo.pop();
      if (notvisited(current)) {
        mark_visited(current);
        for (const T x : neighbors(current)) {
          todo.push(make_pair(x, current));
        }
        end_ = false;
        break;
      }
    }
  }
  T operator*() { return current; }
  T previous() { return prev; }
  bool end() { return end_; }

 private:
  T current;
  T prev;
  bool end_;
};
template <class T>
class Graph {
 public:
  vector<T> vertices;
  vector<set<int>> neighbors;
  depth_first_search_iterator<int> dfs_iterator;
  breadth_first_search_iterator<int> bfs_iterator;
  vector<bool> visited;
  Graph() {}
  Graph(int n) {
    for (int i = 0; i < n; ++i) {
      AddVertex(0);
    }
  }
  void AddVertex(T val) {
    vertices.push_back(val);
    neighbors.push_back(set<int>());
  }
  bool EdgeExists(int i, int j) {
    return (neighbors[i].find(j) != neighbors[i].end());
  }
  void AddEdge(int i, int j) {
    if (!EdgeExists(i, j)) {
      neighbors[i].insert(j);
      if (i != j) {
        neighbors[j].insert(i);
      }
    }
  }
  T& operator[](int i) { return vertices[i]; }
  void RemoveEdge(int i, int j) {
    if (EdgeExists(i, j)) {
      neighbors[i].erase(find(neighbors[i].begin(), neighbors[i].end(), j));
      neighbors[j].erase(find(neighbors[j].begin(), neighbors[j].end(), i));
    }
  }
  void dfs_init(int start) {
    visited = vector<bool>(vertices.size(), false);
    dfs_iterator = depth_first_search_iterator<int>(
        start, [this](int x) { return !visited[x]; },
        [this](int x) { visited[x] = true; },
        [this](int x) { return neighbors[x]; });
  }
  void bfs_init(int start) {
    visited = vector<bool>(vertices.size(), false);
    bfs_iterator = breadth_first_search_iterator<int>(
        start, [this](int x) { return !visited[x]; },
        [this](int x) { visited[x] = true; },
        [this](int x) { return neighbors[x]; });
  }
  void print_() {
    for (int i = (0); i < (0) + (vertices.size()); ++i) {
      for (auto x : neighbors[i]) {
        if (i <= x) {
          cout << i << "-" << x << endl;
        }
      }
    }
  }
};
template <class T>
class DirectedGraph {
 public:
  vector<T> vertices;
  vector<set<int>> neighbors;
  depth_first_search_iterator<int> dfs_iterator;
  breadth_first_search_iterator<int> bfs_iterator;
  vector<bool> visited;
  DirectedGraph() {}
  DirectedGraph(int n) {
    for (int i = 0; i < n; ++i) {
      AddVertex(0);
    }
  }
  bool EdgeExists(int i_from, int j_to) {
    return (neighbors[i_from].find(j_to) != neighbors[i_from].end());
  }
  void AddVertex(T val) {
    vertices.push_back(val);
    neighbors.push_back(set<int>());
  }
  void AddEdge(int i_from, int j_to) {
    if (!EdgeExists(i_from, j_to)) {
      neighbors[i_from].insert(j_to);
    }
  }
  T& operator[](int i) { return vertices[i]; }
  void RemoveEdge(int i_from, int j_to) {
    if (EdgeExists(i_from, j_to)) {
      neighbors[i_from].erase(
          find(neighbors[i_from].begin(), neighbors[i_from].end(), j_to));
    }
  }
  DirectedGraph<T> Transpose() {
    DirectedGraph<T> ret;
    for (auto x : vertices) {
      ret.AddVertex(x);
    }
    for (int i_from = 0; i_from < vertices.size(); ++i_from) {
      for (int j_to : neighbors[i_from]) {
        ret.AddEdge(j_to, i_from);
      }
    }
    return ret;
  }
  int vertices_count() { return vertices.size(); }
  void dfs_init(int start) {
    visited = vector<bool>(vertices.size(), false);
    dfs_iterator = depth_first_search_iterator<int>(
        start, [this](int x) { return !visited[x]; },
        [this](int x) { visited[x] = true; },
        [this](int x) { return neighbors[x]; });
  }
  void bfs_init(int start) {
    visited = vector<bool>(vertices.size(), false);
    bfs_iterator = breadth_first_search_iterator<int>(
        start, [this](int x) { return !visited[x]; },
        [this](int x) { visited[x] = true; },
        [this](int x) { return neighbors[x]; });
  }
  void print_() {
    for (int i = (0); i < (0) + (vertices.size()); ++i) {
      for (auto x : neighbors[i]) {
        cout << i << "->" << x << endl;
      }
    }
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cout.precision(17);
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  uniform_int_distribution<int> rand_gen(0, modd);
  int test_cases = 1;
  for (int t = (1); t < (1) + (test_cases); ++t) {
    int n;
    cin >> n;
    vector<int> a;
    for (int i = (0); i < (0) + (n); ++i) {
      int kk;
      cin >> kk;
      a.push_back(kk);
    }
    int dir = 1, last = -1;
    for (int i = (0); i < (0) + (n); ++i) {
      if (abs(a[i]) % 2 == 1) {
        a[i] += dir;
        dir *= -1;
        last = i;
      }
    }
    vector<int> b;
    for (int x : a) {
      b.push_back(x / 2);
    }
    if (accumulate(b.begin(), b.end(), 0) != 0) {
      b[last] += dir;
    }
    for (auto x : b) {
      cout << x << endl;
    }
  }
  return 0;
}