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: Accepted)

p :: Int -> Int -> [Int] -> Int
p n x (y:[])
  | x + y >= 0 = n+x+y+1
  | otherwise = n
p n x (y:ys)
  | x + y >= 0 = m (n+x+y+1) (-1) ys
  | otherwise = m n (x+y) ys

m :: Int -> Int -> [Int] -> Int
m n x (y:[])
  | x + y <= 0 = n-(x+y)+1
  | otherwise = n
m n x (y:ys)
  | x + y <= 0 = p (n-(x+y)+1) 1 ys
  | otherwise = p n (x+y) ys

solve :: [Int] -> Int
solve (x:xs)
  | x < 0 = min (p (-x+1) 1 xs) (m 0 x xs)
  | x > 0 = min (p 0 x xs) (m (x+1) (-1) xs)
  | x == 0 = min (p 1 (x+1) xs) (m 1 (x-1) xs)

main = getContents >>= print . solve . map read . words . last . lines