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 Control.Applicative
import Data.List

main = do
  _ <- getLine
  as <- (map read) . words <$> getLine

  print $ minimum
    [sum $ zipWith (\a b -> abs (a-b)) (f 0 as True) as,
     sum $ zipWith (\a b -> abs (a-b)) (f 0 as False) as]
     
  where
    f :: Integer -> [Integer] -> Bool -> [Integer]
    f _ [] _ = []
    f ps (x:xs) m =
      if ps * (ps+x) < 0 then
        x : (f (ps+x) xs m)
      else
        if ps > 0 then
          (-ps-1) : (f (-1) xs m)
        else if ps < 0 then
          (-ps+1) : (f 1 xs m)
        else
          if x /= 0 then
            x : (f x xs m)
          else
            if m then
              1 : (f 1 xs m)
            else
              (-1) : (f (-1) xs m)