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 {
  import scala.math._
  
  val n = readInt
  val a = readLine.split(" ").map{_.toInt}
  
  //start != 0
  def solve(start:Int):Long = {
    var ans:Long = 0
    var sum:Long = start.toLong
    for (i <- 1 until n) {
      val presum = sum
      sum += a(i)
      if (sum == 0) {
        ans += 1
        sum = -presum/abs(presum)
      } else {
        val check = (presum/abs(presum))*(sum/abs(sum))
        if (check > 0) {
          ans += abs(sum)+1
          sum = -sum/abs(sum)
        }
      }
    }
    ans
  }
  
  if (a(0) == 0) println(min(solve(1),solve(-1))+1)
  else println(solve(a(0)))

}