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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import           Control.Monad
import qualified Data.ByteString.Char8       as BS
import           Data.Maybe
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM

readInt = fst . fromJust . BS.readInt
getInt = readInt <$> BS.getLine

main = do
  n <- getInt

  as <- VM.new (n+1)
  VM.write as n (0::Int)

  forM_ [0..(n-1)] $ \i -> do a <- getInt
                              VM.write as i a
  let solve i npairs | i == n = return npairs
                     | otherwise = do
                         ai <- VM.read as i
                         ai1 <- VM.read as (i+1)
                         if ai >= 2
                           then do let m = ai `div` 2
                                   VM.write as i (ai-2*m)
                                   solve i (npairs + m)
                           else if ai == 1 && ai1 > 0
                                then do VM.write as i (0::Int)
                                        VM.write as (i+1) (ai1 - 1)
                                        solve (i+1) (npairs+1)
                                else solve (i+1) npairs

  ans <- solve 0 0
  print ans