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)

N=gets.to_i
list=gets.split(" ").map(&:to_i)
sum = 0
res = 0

def sign(i)
  if (i>0) then
    1
  elsif i < 0 then
    -1
  else
    0
  end
end
if(list[0] == 0) then
  temp = 0
  flag= true
  (N-1).times{|i|
    temp += list[i+1]
    if(temp != 0 && flag) then
      res +=1

      if((i+1)%2 == 0) then
        list[0] = sign(list[i+1])
      else
        list[0] = -sign(list[i+1])
      
      end
      flag = false
    end
    if(i == N-2 && flag) then
      res += 1
      list[0]=1
    end
  }
end

N.times{|i|
  before_sum = sum
  sum += list[i]
  if (sum*before_sum> 0) then
    if(sum > 0) then
      res += (sum+1)
      sum = -1
    else
      res += (-sum+1)
      sum = 1
    end
  elsif sum*before_sum==0 then
    if(before_sum < 0 )then
      res += 1
      sum = 1
    elsif(before_sum > 0) then
      sum = -1
      res += 1
    end
  end
}

puts(res)