Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N. The i-th term in the sequence is a_i.
In one operation, you can select a term and either increment or decrement it by one.

At least how many operations are necessary to satisfy the following conditions?

For every i (1≤i≤n), the sum of the terms from the 1-st through i-th term is not zero.

For every i (1≤i≤n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.

Constraints

2 ≤ n ≤ 10^5

|a_i| ≤ 10^9

Each a_i is an integer.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print the minimum necessary count of operations.

Sample Input 1

4
1 -3 1 0

Sample Output 1

4

For example, the given sequence can be transformed into 1, -2, 2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1, 1 and -1, respectively, which satisfy the conditions.

Sample Input 2

5
3 -6 4 -5 7

Sample Output 2

0

The given sequence already satisfies the conditions.

Sample Input 3

6
-1 4 3 2 -5 4

Sample Output 3

8

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust)

main = do
  n <- readLn :: IO Int
  (a:as) <- getIntListBC
  let ans1 = solve a as
      x = (+1) $ abs a
      ans2 = if a >= 0 then x + solve (a-x) as
                       else x + solve (a+x) as
  print $ min ans1 ans2

bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

getIntListBC :: IO [Int]
getIntListBC = map bsToInt . BC.words <$> BC.getLine

solve :: Int -> [Int] -> Int
solve _ []    = 0
solve s (a:as)
  | s > 0     = let n = negate $ s + 1
                in if n > a then solve (s + a) as
                            else (abs $ a - n) + solve (s + n) as
  | s < 0     = let n = negate $ s - 1
                in if n < a then solve (s + a) as
                            else (abs $ n - a) + solve (s + n) as
  | otherwise = 1 + solve 1 as