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.strip.to_i
a = gets.strip.split.map(&:to_i)

cum_a = [a.first]
(1..n-1).to_a.each do |index|
  cum_a[index] = cum_a[index-1]+a[index]
end

minus_first_result = 0
minus_first_base = 0

(0..n-1).to_a.each do |index|
  current = cum_a[index]
  if index.even? && (revised = current+minus_first_base) >= 0
    minus_first_result += (revised+1)
    minus_first_base -= (revised+1)
  elsif index.odd? && (revised = current+minus_first_base) <= 0
    minus_first_result += (-1*revised+1)
    minus_first_base += (-1*revised+1)
  end
end


plus_first_result = 0
plus_first_base=0

(0..n-1).to_a.each do |index|
  current = cum_a[index]
  if index.even? && (revised = current+plus_first_base) <= 0
    plus_first_result += (-1*revised+1)
    plus_first_base += (-1*revised+1)
  elsif index.odd? && (revised = current+plus_first_base) >= 0
    plus_first_result += (revised+1)
    plus_first_base -= (revised+1)
  end
end


p [plus_first_result, minus_first_result].min