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 (2.7.1) (judge verdict: Wrong Answer)

# n + 1 長の array を返す
def cumulative_sum(array)
  tmp = [0]
  previous = 0
  array.each { |num| tmp << previous += num }
  tmp
end

def ans(cumulative_sums, previous_plus, ans, added)
  cumulative_sums.each do |sum|
    if previous_plus && sum + added >= 0
      ans += (sum + added).abs + 1
      added -= (sum + added).abs + 1
    elsif !previous_plus && sum + added <= 0
      ans += (sum + added).abs + 1
      added += (sum + added).abs + 1
    end
    previous_plus = !previous_plus
  end
  ans
end

n = gets.to_i
nums = gets.split.map(&:to_i)
cumulative_sums = cumulative_sum(nums)
cumulative_sums.delete_at(0)
first = cumulative_sums.delete_at(0)
answers = []
if first > 0
  answers << ans(cumulative_sums, true, 0, 0)
elsif first < 0
  answers << ans(cumulative_sums, false, 0, 0)
else
  answers << ans(cumulative_sums, true, 1, 1)
  answers << ans(cumulative_sums, false, 1, -1)
end

puts answers.min