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 (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt()
  val as = List.fill(n)(sc.nextLong())

  def solve(sgn: Int): Long = {
    var sum = 0L
    var ans = 0L
    if (sgn * as.head <= 0) {
      sum = sgn
      ans += as.head.abs + 1
    } else {
      sum = as.head
    }

    for (a <- as.tail) {
      if ((sum > 0 && sum + a >= 0) || (sum < 0 && sum + a <= 0)) {
        ans += (if (sum > 0) sum + a + 1 else -(sum + a - 1))
        sum = if (sum > 0) -1 else 1
      } else {
        sum += a
      }
    }
    ans
  }

  println(solve(1).min(solve(-1)))
}