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 OCaml (4.02.3) (judge verdict: Accepted)

open Batteries
let n = Scanf.scanf "%d" (fun x -> x)
let a = List.init n (fun _ -> Scanf.scanf " %d" (fun x -> x))
let rec solve acc sum sign = function
  | [] -> acc
  | (x::xs) ->
      if (sum+x) * sign > 0 then
        solve acc (sum+x) (-sign) xs
      else
        let acc' = acc + abs (sum+x - sign) in
        solve acc' sign (-sign) xs

let () =
  min (solve 0 0 1 a) (solve 0 0 (-1) a)
  |> Printf.printf "%d\n"