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: Accepted)

import scala.io.StdIn
import scala.annotation.tailrec

object Main extends App {
  val n = StdIn.readInt
  val a = StdIn.readLine.split(" ").map(_.toLong)

  // 1項目が 0 の時は 1 か -1 に変える
  val init1 = if(a.head <= 0) 1 - a.head else 0
  val ans1 = a.tail./:(a.head + init1, init1.abs)((acc,i) => {
    val (bsum, bcnt) = acc
    val sum = bsum + i
    val cnt = if(bsum < 0 && sum < 0) 1 - sum
    else if(bsum > 0 && sum > 0) -1 - sum
    else if(sum == 0) if(bsum < 0) 1 else -1
    else 0
    (sum+cnt, bcnt+cnt.abs)
  })._2

  val init2 = if(a.head < 0) 0 else -1 - a.head
  val ans2 = a.tail./:(a.head + init2, init2.abs)((acc,i) => {
    val (bsum, bcnt) = acc
    val sum = bsum + i
    val cnt = if(bsum < 0 && sum < 0) 1 - sum
    else if(bsum > 0 && sum > 0) -1 - sum
    else if(sum == 0) if(bsum < 0) 1 else -1
    else 0
    (sum+cnt, bcnt+cnt.abs)
  })._2

  println(math.min(ans1, ans2))
}