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())
evenar=[]
oddar=[]
ar=[]
ar1=[]
sum1=0
sum2=0
sumi=0
for i in range(n):
    s=int(input())
    ar.append(s)
    
    if(s%2==0):
        evenar.append(s//2)
        
    else:
        oddar.append(s//2)
      
for j in range(len(evenar)):
    sum1=sum1+evenar[j]
    
for j in range(len(oddar)):
    sum2=sum2+oddar[j]
    
sum=sum1+sum2
a=abs(sum)

for i in range(len(ar)):
    ar1.append(ar[i]//2)


if(sum==0):
    for i in range(len(ar1)):
        print(ar1[i])
elif(sum<0):
    i=0
    while(a!=0  and i<len(ar)):
        
        if(ar[i]%2!=0):
            ar1[i]=ar1[i]+1
            a=a-1
        i=i+1
    for k in range(len(ar1)):
        print(ar1[k])
else:
    i=0
    while(a!=0 and i<len(ar)):
        if(ar[i]%2!=0):
            ar1[i]=ar1[i]-1
            a=a-1
        i=i+1
    for k in range(len(ar1)):
        print(ar1[k])