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 solve(n, a)
  (n-1).times{|i|a[i+1]+=a[i]}
  sum=res=0
  (n-1).times do |i|
    a[i+1] += sum
    next if a[i]*a[i+1]<0
    if a[i+1]==0
      res += 1
      sum -= a[i]/a[i].abs
    else
      res += a[i+1].abs + 1
      sum -= a[i+1] + a[i+1]/a[i+1].abs
    end
    a[i+1] = -a[i]/a[i].abs
  end
  return res
end

n=gets.to_i
a=gets.split.map &:to_i
if a[0]!=0
  p solve(n, a)
else
  a[0]=1
  s1 = 1+solve(n, a.dup)
  a[0]=-1
  s2 = 1+solve(n, a.dup)
  p [s1, s2].min
end