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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val _ = readLine
    val datA = readLine.split(" ").map(_.toInt)

    val work = datA.map(a => (a, 0)).foldLeft((0, 0)){ case ((sum, count),(a, _)) =>
      if (sum > 0) {
        if (sum + a >= 0) (-1, count + math.abs(sum + a) + 1)
        else (sum + a, count)
      }
      else if (sum < 0) {
        if (sum + a <= 0) (1, count + math.abs(sum + a) + 1)
        else (sum + a, count)
      } else {
        (a, count)
      }
    }

    val ans = work._2
    println(ans)
  }
}