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 math
n = int(input())
a = []
for i in range(n):
    a.append(int(input()))

b = []
c = []

for i in range(n):
    if a[i]%2 != 0:
        if a[i]>0:
            b.append(i)
        elif a[i]<0:
            c.append(i)
    else:
        a[i] = a[i]//2

n1 = len(b)
for i in range(n1//2):
    a[b[i]] = int(math.floor(a[b[i]]/2))
    a[b[n1-1-i]] = int(math.ceil(a[b[n1-1-i]]/2))

if n1%2!=0:
    a[b[n1//2]] = int(math.floor(a[b[n1//2]]/2))

n2 = len(c)
for i in range(n2//2):
    # print(c[i],c[n2-1-i],int(math.ceil(a[c[i]]/2)),int(math.floor(a[c[i]]/2)))
    a[c[i]] = int(math.floor(a[c[i]]/2))
    a[c[n2-1-i]] = int(math.ceil(a[c[n2-1-i]]/2))

if n2%2!=0:
    # print('hey')
    a[c[n2//2]] = int(math.ceil(a[c[n2//2]]/2))

# print(b,n1)
# print(c,n2)

for i in range(n):
    print(a[i])