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 int M = 1000000007;
long long int i, j;
long long int fac(long long int x);
long long int inv_fac(long long int x);
long long int binexp(long long int a, long long int b);
long long int fac(long long int x) {
  long long int fcto = 1;
  for (long long int i = 2; i <= x; i++) {
    fcto *= i;
    fcto %= M;
  }
  return fcto;
}
long long int inv_fac(long long int x) { return binexp(fac(x), M - 2); }
long long int binexp(long long int a, long long int b) {
  if (a == 0 || a == 1) return a;
  if (b == 0) return 1;
  long long int ret = binexp(a, b / 2);
  if (b % 2)
    return (((ret * ret) % M) * a) % M;
  else
    return (ret * ret) % M;
}
bool sortbysecdesc(const pair<int, int> &a, const pair<int, int> &b) {
  return a.second > b.second;
}
long long int isPrime(long long int n) {
  if (n <= 3) return (1);
  if (n % 2 == 0 || n % 3 == 0) return (0);
  for (i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return (0);
  return (1);
}
long long int smallestDivisor(long long int n) {
  if (n % 2 == 0) return 2;
  for (i = 3; i * i <= n; i += 2) {
    if (n % i == 0) return i;
  }
  return n;
}
long long maxPrimeFactors(long long n) {
  long long maxPrime = -1;
  while (n % 2 == 0) {
    maxPrime = 2;
    n >>= 1;
  }
  for (i = 3; i <= sqrt(n); i += 2) {
    while (n % i == 0) {
      maxPrime = i;
      n = n / i;
    }
  }
  if (n > 2) maxPrime = n;
  return maxPrime;
}
long long int countDivisors(long long int n) {
  long long int cnt = 0;
  for (i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(NULL), cout.tie(NULL);
  long long int t = 1;
  while (t--) {
    long long int n;
    cin >> n;
    long long int sum = 0;
    map<long long int, long long int> mp;
    long long int a[n];
    for (i = 0; i < n; i++) {
      cin >> a[i];
      if (a[i] > 0 && a[i] % 2 == 1) {
        mp[i]++;
        a[i] /= 2;
      } else if (a[i] < 0 && (-1 * a[i]) % 2 == 1) {
        mp[i]++;
        long long int num = (-1 * a[i]) / 2;
        a[i] = (-1) * num;
        if (a[i] == 0) {
          mp[i]++;
        }
      } else {
        if (a[i] >= 0) {
          a[i] = a[i] / 2;
        } else {
          long long int num = -a[i];
          num /= 2;
          a[i] = (-1) * num;
        }
      }
      sum += a[i];
    }
    if (sum > 0) {
      for (i = 0; i < n; i++) {
        if (mp[i] == 1 && a[i] < 0) {
          a[i] -= 1;
          sum -= 1;
        } else if (mp[i] == 2 && a[i] == 0) {
          a[i] -= 1;
          sum -= 1;
        }
        if (sum == 0) {
          break;
        }
      }
    } else if (sum < 0) {
      for (i = 0; i < n; i++) {
        if (mp[i] == 1 && a[i] >= 0) {
          a[i] += 1;
          sum++;
        }
        if (sum == 0) {
          break;
        }
      }
    }
    for (i = 0; i < n; i++) {
      cout << a[i] << "\n";
    }
  }
}