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:
from math import sqrt
def main():
    n = int(input())
    nodd = 0
    podd = 0
    a = []
    ans = []
    sm = 0
    for i in range(n):
        ai = int(input())
        if(ai < 0):
            x = ai//2

        else:
            if(ai%2==1):
                x = (ai+1)//2
            else:
                x = ai//2

        sm += x
        a.append(ai)
        ans.append(x)

    if(sm < 0):
        for i in range(n):
            if(abs(a[i])%2==1 and ans[i]<0):
                ans[i] += 1
                sm += 1
            if(sm==0):
                break
            
    elif(sm > 0):
        for i in range(n):
            if(a[i]%2==1 and ans[i]>0):
                ans[i] -= 1
                sm -= 1
            if(sm==0):
                break

    for i in ans:
        print(i)
        

    
if __name__ =="__main__":
    main()