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)

after [] n = 1
after as n
  | head as == 0 = after (tail as) (n + 1)
  | head as < 0 = if odd n then 1 else (-1)
  | head as > 0 = if odd n then (-1) else 1

solve [] v acc = acc
solve as v acc
  | v == 0 =
    if after as 0 < 0
      then solve as 1 (1 + acc)
      else solve as (-1) (1 + acc)
  | v < 0 =
    let w = v + (head as) in
      if w <= 0
        then solve (tail as) 1 (1 - w + acc)
        else solve (tail as) w acc
  | v > 0 =
    let w = v + (head as) in
      if w >= 0
        then solve (tail as) (-1) (1 + w + acc)
        else solve (tail as) w acc

main = do
  n <- read <$> getLine :: IO Int
  l <- getLine
  let as = fmap read (words l) :: [Int] in
    putStrLn (show (solve (tail as) (head as) 0))