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:
# def climbingLeaderboard(scores, alice):
#         l=[]
#         s=sorted(set(scores),reverse=True)
#         j=0
#         for i in alice:
#             for k in range(j,len(s)):
#                 print("ele:",s[k])
#                 if i>=s[k]:
#                     l.append(k)
#                     break
#                 else:
#                     continue
#         return(l)
# scores_count = int(input())

# scores = list(map(int, input().rstrip().split()))

# alice_count = int(input())

# alice = list(map(int, input().rstrip().split()))

# result = climbingLeaderboard(scores, alice)

# print(result)
import math
l=[]
for i in range(int(input())):
	l.append(int(input()))
def fun(a,c):
	if(a%2==0):
		return a/2
	elif (c%2==0):
		return int(a-1/2)
	elif (c%2!=0):
		return int(a+1/2)
count=0
for i in l:
	if(i%2==0):
		i=int(i/2)
		print(i)
	elif (count%2==0):
		i=int((i-1)/2)
		count+=1
		print(i)
	elif (count%2!=0):
		i=int((i+1)/2)
		count+=1
		print(i)