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: Accepted)

_n = gets.to_i
as = gets.split.map(&:to_i)
sum = 0
calc = as.map { |num|
  sum += num
}

# calc[0]、つまりevenを正とする場合
change = 0
moved = 0
calc.map.with_index { |num, i|
  if i.even?
    if num + change > 0
      # 問題なし
    else
      diff = 1 - (num+change)
      change += diff
      moved += diff.abs
    end
  else # i.odd?
    if num + change < 0
      # 問題なし
    else
      diff = -1 - (num+change)
      change += diff
      moved += diff.abs
    end
  end
}
even_moved = moved

# calc[1]、つまりoddを正とする場合
change = 0
moved = 0
calc.map.with_index { |num, i|
  if i.odd?
    if num + change > 0
      # 問題なし
    else
      diff = 1 - (num+change)
      change += diff
      moved += diff.abs
    end
  else # i.even?
    if num + change < 0
      # 問題なし
    else
      diff = -1 - (num+change)
      change += diff
      moved += diff.abs
    end
  end
}
odd_moved = moved

puts [even_moved, odd_moved].min