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 extends App {
  val scan = new java.util.Scanner(System.in)
  val n  = scan.next().toInt
  val ns = (1 to n).map(_ => scan.next().toInt)

  var even_sum = 0
  var even_cnt = 0
  for (i <- 0 until n) {
    even_sum += ns(i)
    if (i%2 == 0) {
      if (even_sum == 0) {
        even_sum += 1
        even_cnt += 1
      } else if (even_sum < 0) {
        even_cnt += 1-even_sum
        even_sum = 1
      }
    } else {
      if (even_sum == 0) {
        even_sum -= 1
        even_cnt += 1
      } else if (even_sum > 0) {
        even_cnt += 1+even_sum
        even_sum = -1
      }
    }
  }

  var odd_sum = 0
  var odd_cnt = 0
  for (i <- 0 until n) {
    odd_sum += ns(i)
    if (i%2 != 0) {
      if (odd_sum == 0) {
        odd_sum += 1
        odd_cnt += 1
      } else if (odd_sum < 0) {
        odd_cnt += 1-odd_sum
        odd_sum = 1
      }
    } else {
      if (odd_sum == 0) {
        odd_sum -= 1
        odd_cnt += 1
      } else if (odd_sum > 0) {
        odd_cnt += 1+odd_sum
        odd_sum = -1
      }
    }
  }
  println(math.min(odd_cnt, even_cnt))
}