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:
n=int(input())
l=[int(input()) for i in range(n)]
pos=[]
neg=[]
for i in l:
    if i>=0:
        pos.append(i)
    else:
        neg.append(abs(i))
op=sum(i%2 for i in pos)
on=sum(abs(i)%2 for i in neg)
if op==on:
    for i in l:
        if i>=0:
            print(i//2)
        else:
            n=abs(i)
            print(-(n//2))
if op>on: 
    r=op-on 
    c=0 
    a=r//2 
    for i in l:
        if i>=0 :
            if i&1:
                if c<a: 
                    print(i//2+1)
                    c+=1 
                else:
                    print(i//2)
            else:
                print(i//2)
        else:
            n=abs(i)
            print(-(n//2))
if op<on: 
    r=on-op
    a=r//2 
    c=0 
    for i in l: 
        if i>=0: 
            print(i//2)
        else: 
            n=abs(i)
            if n&1:
                if c<a: 
                    print(-(n//2+1))
                    c+=1 
                else: 
                    print(-(n//2))
            else: 
                print(-(n//2))