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
import math
import bisect
import math
from itertools import accumulate
 
input = sys.stdin.readline
def inpit(): #int
    return(int(input()))
def inplt(): #list 
    return(list(map(int,input().split())))
def inpstr(): #string
    s = input()
    return(list(s[:len(s) - 1]))
def inpspit(): #spaced intergers 
    return(map(int,input().split()))
 
pow = math.pow
fl = math.floor
ceil = math.ceil
dis = math.hypot # cartesian distance 

def lcm(a):
    return abs(math.prod(a)) // math.gcd(*a)
 
def cumulativeSum(input): # prefix sum
      return (list(accumulate(input))) 





t = inpit()
lt = []
for i in range(t):
    lt.append(inpit())

b = 0
for i in range(t):
    if(lt[i]%2 == 0):
        lt[i] = lt[i]/2
    else:
        if(b <0):
            lt[i] = math.ceil(float(lt[i])/2.0)
            b = b +1 

        elif(b >0):
            lt[i] = math.floor(float(lt[i])/2.0)
            b = b -1 
        elif(b == 0):
            lt[i] = math.ceil(float(lt[i])/2.0)
            b = b +1




for i in lt:
    print(int(i))