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:
from math import ceil, floor
n = int(input())

ori = []
fin = []

s = 0
lower = False
for i in range(n):
    e = int(input())
    ori.append(e)
    if e >=0:
        if e % 2 == 0:
            to_add = e // 2
            s+= to_add
            fin.append(to_add)
        else:
            if lower:
                to_add = floor(e /2)
                fin.append(to_add)
                s+= to_add
            else:
                to_add = ceil(e / 2)
                fin.append(to_add)
                s+=to_add
            lower = not lower
    else:
        fin.append(e)

index = 0    
lower = False    
for i in range(n):
    e = fin[i]
    if e < 0:
        if e % 2 == 0:
            to_add = e // 2
            fin[i] = to_add
            s+=to_add
        else:
            index = i
            if lower:
                to_add = floor(e / 2)
                fin[i] = to_add
                s+=to_add
            else:
                to_add = ceil(e / 2)
                fin[i] = to_add
                s+= to_add
            lower = not lower

fin[index] -=s
for i in fin:
    print(i)