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
a = gets.chomp.split(" ").map(&:to_i)
count = 0
sum = 0#a[0]
i=1
if a[0] == 0
count = 1

for i in 1..a.size-1
  break if a[i] != 0
  count += 2
end

if a[i] > 0
  sum = -1
elsif a[i]==0
  count -= 1
else
  sum = 1
end
else
sum = a[0]
end

for i in i..a.size-1
  newsum = sum + a[i]
  #p [sum,newsum]
  if sum >= 0 && newsum >= 0
    count += ( 1 + newsum)
    newsum = -1
    #p count
  elsif sum <= 0 && newsum <= 0
    count -= -1 + newsum
    newsum = 1
    #p count
  else
  end
  #p [sum,newsum]
    sum = newsum
end

p count