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 (2.7.1) (judge verdict: Accepted)

def calc(n, a, init_sum, init_count)
  prev_sum = init_sum
  count = init_count
  for i in 1...n do
    sum = prev_sum + a[i]
    if prev_sum * sum >= 0
      count += sum.abs + 1
      sum = prev_sum > 0 ? -1 : 1
    end
#    puts [sum, count].join(" ")
    prev_sum = sum
  end
  return count
end

n = gets.to_i
a = gets.split.map(&:to_i)
count1 = count2 = 0
if a[0] != 0
  count1 = calc(n, a, a[0], 0)
  count2 = calc(n, a, (a[0] > 0 ? -1 : 1), a[0].abs + 1)
else
  count1 = calc(n, a, 1, 1)
  count2 = calc(n, a, -1, 1)
end
#puts [count1, count2].join(" ")
puts [count1, count2].min