Problem:
Score : 400 points

Problem Statement

Snuke has a large collection of cards. Each card has an integer between 1 and N, inclusive, written on it.
He has A_i cards with an integer i.

Two cards can form a pair if the absolute value of the difference of the integers written on them is at most 1.

Snuke wants to create the maximum number of pairs from his cards, on the condition that no card should be used in multiple pairs. Find the maximum number of pairs that he can create.

Constraints

1 ≦ N ≦ 10^5

0 ≦ A_i ≦ 10^9 (1 ≦ i ≦ N)

All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum number of pairs that Snuke can create.

Sample Input 1

4
4
0
3
2

Sample Output 1

4

For example, Snuke can create the following four pairs: (1,1),(1,1),(3,4),(3,4).

Sample Input 2

8
2
0
1
6
0
8
2
1

Sample Output 2

9

Solution in Ruby (2.3.3) (judge verdict: Memory Limit Exceeded)

n = gets.chomp.to_i
cards_p = []
$count = 0
n.times do |i|
  num = gets.chomp.to_i
  if num > 0
    cards_p << [i+1] * num
  end
end
cards_p.flatten!

def search(cards)
  if cards.size <= 1
    return
  end
#  p cards
  0.upto(cards.size-2) do |idx|
#    puts %(#{idx},#{idx+1})
#    puts %(#{cards[idx]},#{cards[idx+1]})

    if (cards[idx] - cards[idx+1]).abs <= 1
      $count += 1
      cards.delete_at(idx)
      cards.delete_at(idx)
#      p cards
#      gets
      break
#      search(cards)
    end
#    p cards
#  if (a - b).abs <= 1
#    count += 1
#  end
  end
  if cards.size <= 2
    return
  end
  search(cards)
end

cards_p.size.times do
  search(cards_p)
end

puts $count
#p cards_p