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 io, sys, atexit, os
import math as ma
from sys import exit
from decimal import Decimal as dec
from itertools import permutations
from itertools import combinations


def li ():
	return list (map (int, sys.stdin.readline ().split ()))


def num ():
	return map (int, sys.stdin.readline ().split ())


def nu ():
	return int (input ())


def find_gcd ( x, y ):
	while (y):
		x, y = y, x % y
	return x


def lcm ( x, y ):
	gg = find_gcd (x, y)
	return (x * y // gg)

mm = 1000000007
fact_powers=[0]*19
tset=set()

def go ( ind, x ):
	if (ind == 19):
		tset.add (x)
		return

	if (x in tset):
		return
	go (ind + 1, x)
	i = 0
	for xx in fact_powers [ ind ]:
		p = x * xx
		if (p >1e18):
			break
		go (ind + 1, p)

def solve ():
	t = 1
	for tt in range (t):
		n=nu()
		zp=1
		for i in range(n):
			p=nu()
			if(p%2==0):
				print(p//2)
			else:
				if(zp==1):
					op=int(ma.floor(p/2))
					print(op)
					zp*=-1
				else:
					op = int (ma.ceil (p / 2))
					print (op)
					zp *= -1






if __name__ == "__main__":
	solve ()