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: Time Limit Exceeded)

open Batteries
let () =
  let n = Scanf.scanf "%d " (fun a -> a) in
  let a_lst = Array.to_list @@ Array.init n (fun _ -> Scanf.scanf "%d " (fun a -> a)) in

  let rec aux sum sign cnt l =
    match l with
    | [] -> cnt
    | hd :: tl -> match sign with
      | `Plus -> 
        if sum + hd <= 0 then aux sum sign (cnt+1) (hd+1::tl) else aux (sum+hd) `Minus cnt tl
      | `Minus -> 
        if sum + hd >= 0 then aux sum sign (cnt+1) (hd-1::tl) else aux (sum+hd) `Plus cnt tl
  in

  Printf.printf "%d\n" @@
  aux 0 (if List.hd a_lst > 0 then `Plus else `Minus) 0 a_lst