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 8.8.3) (judge verdict: Accepted)

import Data.List
import Data.Maybe
import qualified Data.ByteString.Char8 as B
main=print.solve.map(fst.fromJust.B.readInt).B.words=<<B.getContents
solve(n:a:as)=minimum$map(\f->fst$foldl' g(f 0 a)as)[fp,fn]
ft c b v=(c+abs(b-v),v)
fp c b=ft c b$max 1 b
fn c b=ft c b$min(-1)b
g(c,p)a
  |p<0=fp c$p+a
  |p>0=fn c$p+a