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
a = gets.chomp.split.map(&:to_i)
sum1 = 0
sum2 = 0
ans = 0
for i in 0..n-2
  sum1 += a[i]
  if sum1 == 0
    if a[i+1] > 1
      a[i] -= 1
      sum1 -= 1
      ans += 1
    else
      a[i] += 1
      sum1 += 1
      ans += 1
    end
  end
  sum2 = sum1 + a[i+1]
  if sum2 * sum1 >= 0
    if sum1 < 0
      if sum1 <= sum2
        a[i+1] += 1 - sum2
        ans += 1 - sum2
      else
        a[i] += -sum1 + 1
        ans += -sum1 + 1
        sum1 = 1
      end
    else
      if sum1 >= sum2
        a[i+1] -= sum2 + 1
        ans += sum2 + 1
      else
        a[i] -= 1 + sum1
        ans += 1 + sum1
        sum1 = -1
      end
    end
  end
end
puts a.join(" ")
puts ans