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 PYTHON3):

Solution:
import sys
input = sys.stdin.readline

def main():
    n = int(input())
    a = []
    for _ in range(n):
        a.append(int(input()))

    c_mi_odd = 0
    c_pl_odd = 0

    for i in a:
        if i > 0 and i % 2 == 1:
            c_pl_odd += 1
        elif i < 0 and i % 2 == 1:
            c_mi_odd += 1

    c_pl_odd %= 2
    c_mi_odd %= 2

    pl_next_up = True
    mi_next_up = False
    if c_pl_odd == c_mi_odd:
        pl_next_up = False


    for i, v in enumerate(a):
        if v % 2 == 0:
            print(v // 2)
        else:
            if v > 0:
                if pl_next_up:
                    print(v // 2)
                    pl_next_up = False
                else:
                    print(-(-v // 2))
                    pl_next_up = True
            else:
                if mi_next_up:
                    print(-(-v // 2))
                    mi_next_up = False
                else:
                    print(v // 2)
                    mi_next_up = True


if __name__ == '__main__':
    main()