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)

module Main(main) where

import Control.Applicative
import Control.Monad
import Data.List
import Data.Array
import Data.Char
import qualified Data.Set as S

main = do
  n <- (read::String -> Int) <$> getLine
  arr <- map (read::String -> Int) . words <$> getLine
  print $ calcCost arr


calcCost::[Int] -> Int
calcCost (x:xs)
  | x /= 0 = snd $ foldl (\(s, c) v -> let next = calcNext s in if next * v > 0 && abs v > abs next then (s + v, c) else (s + next, c + abs (next - v))) (x, 0) xs
  | otherwise = let plus = 1 + calcCost (1:xs)
                    minus = 1 + calcCost ((-1):xs)
                in min plus minus

calcNext::Int -> Int
calcNext a = if a > 0 then -a - 1 else -a + 1