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
arr = gets.chomp.split(" ").map(&:to_i)

$count = 0

def check(i,arr,t)
  if i > arr.size - 1
    arr[t] += 1
    $count += 1
    return
  end
  if arr[i] > 0
    arr[t] -= 1
    $count += 1
  elsif arr[i] < 0
    arr[t] += 1
    $count += 1
  else
    check(i+1,arr,t)
  end
end


sum = arr[0] + arr[1]
if sum == 0
    check(2,arr,1)
end

sum = arr[0] + arr[1]

(2...arr.size).each do |i|
  diff = sum + arr[i]
#  puts %(sum : #{sum})
#  puts %(diff : #{diff})
  if sum > 0
    if diff > 0
      arr[i] -= diff.abs+1
      $count += diff.abs+1
    elsif diff == 0
      check(i+1,arr,i)
    end
  else
    if diff < 0
      arr[i] += diff.abs+1
      $count += diff.abs+1
    elsif diff == 0
      check(i+1,arr,i)
    end
  end
  sum += arr[i]
end

#p arr
puts $count