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: Accepted)

def sign(i)
  return 1 if i.positive? || i == 0
  -1
end

def sequence(n, arr)
  a = arr
  b = [ a[0] ]
  count = 0

  (n-1).times do |i|
    b[i+1] = b[i] + a[i+1]
    if b[i+1] == 0
      if b[i] > 0
        a[i+1] -= 1
        count += 1
      else
        a[i+1] += 1
        count += 1
      end
    elsif sign(b[i]) == sign(b[i+1])
      if b[i].positive?
        count += (a[i+1] - (-b[i] - 1)).abs
        a[i+1] = -b[i] - 1
        b[i+1] = b[i] + a[i+1]
      else
        count += (a[i+1] - (-b[i] + 1)).abs
        a[i+1] = -b[i] + 1
        b[i+1] = b[i] + a[i+1]
      end
    end
  end

  count
end

n = gets.chomp.to_i
a = gets.chomp.split.map { |item| item.to_i }
a2 = Marshal.load(Marshal.dump(a))
pn_count = 0

if a[0] > 0
  a2[0] = a[0] - a[0] - 1
  np_count = a[0].abs + 1
elsif a[0] < 0
  a2[0] = a[0] - a[0] + 1
  np_count = a[0].abs + 1
else
  a[0] = 1
  pn_count = 1
  a2[0] = -1
  np_count = 1
end

pn_count += sequence(n, a)
np_count += sequence(n, a2)

puts pn_count < np_count ? pn_count : np_count