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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

io = STDIN
$n=io.gets.chomp.to_i
$a=io.gets.chomp.split.map(&:to_i)
$b=[]
$a.unshift 0
sm=0
(1..$n).each do |i|
  sm+=$a[i]
  $b<<sm
end
def adjust(b,i,delta)
  (i..($n-1)).each do |j|
    b[j]+=delta
  end
  b
end
def calc(ar)
  cnt=0
  ($n-1).times do |i|
    delta=0
    if ar[i]>0 && ar[i+1]<0
    elsif ar[i]<0 && ar[i+1]>0
    elsif ar[i]>0 && ar[i+1]>0
      delta =-(ar[i+1]+1)
    elsif ar[i]<0 && ar[i+1]<0
      delta =(ar[i+1].abs+1)
    else
      if ar[i]>0
        delta=-1
      else
        delta=1
      end
    end
    (ar = adjust(ar,i+1,delta)) unless delta==0
    cnt+=delta.abs
  end
  cnt
end
if $a[1]==0
  b1=$b.clone
  b2=$b.clone
  puts [calc(adjust(b1,0,1)),calc(adjust(b1,0,-1))].min
else
  puts calc($b)
end
__END__