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: Wrong Answer)

n = gets.to_i
as = gets.split.map(&:to_i)

cnt1 = 0
sum = as[0]
n.times.with_index(1) do |_,i|
  break if as[i].nil?
  if sum < 0
    if sum + as[i] > 0
      sum += as[i]
      next
    else
      x = 1 - sum - as[i]
      cnt1 += x
      sum = 1
    end
  elsif sum > 0
    if sum + as[i] < 0
      sum += as[i]
      next
    else
      x = -1 - sum - as[i]
      cnt1 += x.abs
      sum = -1
    end
  end
end

cnt2 = (as[0] * 2).abs
sum = as[0] * -1
n.times.with_index(1) do |_,i|
  break if as[i].nil?
  if sum < 0
    if sum + as[i] > 0
      sum += as[i]
      next
    else
      x = 1 - sum - as[i]
      cnt2 += x
      sum = 1
    end
  elsif sum > 0
    if sum + as[i] < 0
      sum += as[i]
      next
    else
      x = -1 - sum - as[i]
      cnt2 += x.abs
      sum = -1
    end
  end
end
puts [cnt1, cnt2].min