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.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as B
import Data.Char

solve :: VU.Vector Int -> Int -> Int
solve vec n
    | VU.length vec == 2 && VU.sum vec == 0 = 1
    | VU.length vec == 2 && VU.sum vec /= 0 = 0
    | otherwise = minimum $ map fst [f, g]
    where
        t = VU.take 2 vec
        d = VU.drop 2 vec
        f = VU.foldl' step (fst $ init t) d 
        g = VU.foldl' step (snd $ init t) d 
        init :: VU.Vector Int -> ((Int, Int), (Int, Int))
        init vec
            | a + b == 0 = ((1, 1), (1, negate 1))
            | a + b > 0 = ((0, a + b), (1 + a + b, negate 1))
            | otherwise =  ((0, a + b), (abs (1 - (a+b)), 1))
            where
                a = VU.head vec
                b = VU.last vec
        step :: (Int, Int) -> Int -> (Int, Int)
        step (res, acc) x
            | acc + x == 0 = (res + 1, negate (signum acc))
            | (signum acc) /= signum (acc + x) = (res, acc + x)
            | otherwise =
                let
                    aim = negate $ signum acc
                    y = aim - (acc + x)
                in
                    (res + abs y, aim)

main = do
    n <- readLn :: IO Int
    as <- VU.unfoldrN n (B.readInt . B.dropWhile isSpace) <$> B.getLine
    print $ solve as n