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)

def f(a)
  g = lambda{|car, cdr, total=0|
    sum = car
    r = [car]

    cdr.each{|curr|
      if sum >= 0
        r << new_curr = [curr, -sum-1].min
        sum += new_curr
        total += curr - new_curr
      else
        r << new_curr = [curr, -sum+1].max
        sum += new_curr
        total += new_curr - curr
      end
    }
    # p r
    total += 1 if sum == 0
    total
  }
  x = g.(a[0], a[1..-1])
  y = g.(a[0] > 0 ? -1 : 1, a[1..-1], a[0].abs+1)
  [x, y].min
end

N = gets.to_i
A = gets.split.take(N).map(&:to_i)
p f(A)