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:
"""
NTC here
"""
from sys import stdin, setrecursionlimit
setrecursionlimit(10**7)


def iin(): return int(stdin.readline())
 
 
def lin(): return list(map(int, stdin.readline().split()))


# range = xrange
# input = raw_input


def main():
    n=iin()
    a=[iin() for i in range(n)]
    na=[[a[i]//2,i] for i in range(n)]
    sm=0
    for i ,j in na:
        sm+=i
    pv=[]
    for i in range(n):
        if a[i]>0 and a[i]%2:
            pv.append(na[i])
    nv=[]
    for i in range(n):
        if a[i]<0 and a[i]%2:
            nv.append(na[i])
    #print(pv,nv)
    sm=abs(sm)
    l=min(len(nv),sm)
    for i in range(l):
        na[nv[i][1]][0]+=1
    if l<sm:
        l2=len(pv)
        for i in range(min(l2,sm-l)):
            na[pv[i][1]][0]+=1
    


    for i,j in na:
        print(i)
        


main()
# try:
#     main()
# except Exception as e: print(e)