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)

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

num1 = 0
sum1 = 0
A.each_with_index do |a, i|
  sum1 += a
  # +, -, +, -
  if i % 2 == 0
    # +
    if sum1 > 0
      next
    else
      num1 += (1 - sum1).abs
      sum1 = 1
    end
  else
    # -
    if sum1 < 0
      next
    else
      num1 += (-1 - sum1).abs
      sum1 = -1
    end
  end
end

num2 = 0
sum2 = 0
A.each_with_index do |a, i|
  sum2 += a
  # -, +, -, +
  if i % 2 == 0
    # -
    if sum2 < 0
      next
    else
      num2 += (-1 - sum2).abs
      sum2 = -1
    end
  else
    # +
    if sum2 > 0
      next
    else
      num2 += (1 - sum2).abs
      sum2 = 1
    end
  end
end

puts [num1, num2].min