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)

main :: IO ()
main = do
    _ <- readLn :: IO Int
    (a0:as) <- (map read . words) <$> getLine
    print $ solve (0, a0, as)

solve :: (Int, Int, [Int]) -> Int
solve (x, 0, 0:as) = min (solve (x+1, 1, as)) (solve (x+1, -1, as))
solve (x, _, []) = x
solve (x, s, a0:as) = solve (x+k, s + a0 + k, as)
    where
      m = - sign s
      k = if s * a0 > 0 then m - (s + a0) else 0

sign :: Int -> Int
sign x = x `div` abs x