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)

gets
xs = gets.split(' ').map(&:to_i)

def flip_sign(v)
  v > 0 ? -1 : 1
end

def sign(v)
  v > 0 ? 1 : -1
end

a = xs[1..-1].inject([xs.first,0]){|r,v|
  sum = r.first
  count = r.last
  s = sign(sum)
  sum += v
  fs = sign(sum)
  if s == fs
    count += sum.abs + 1
    sum = flip_sign(s)
  end
  [sum, count]
}.last

b = xs[1..-1].inject([flip_sign(xs.first),xs.first.abs + 1]){|r,v|
  sum = r.first
  count = r.last
  s = sign(sum)
  sum += v
  fs = sign(sum)
  if s == fs
    count += sum.abs + 1
    sum = flip_sign(s)
  end
  [sum, count]
}.last
puts [a,b].min