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: Time Limit Exceeded)

object Main {
  def main(args: Array[String]): Unit = {
    solve2
  }
  def solve2(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    sc.nextLine
    val a = sc.nextLine.split(" ").map(_.toInt).toList

    var sum = 0L
    var opeCount1 = 0L
    // 正、負、正、負（偶数インデックスが正）とする
    for (i <- 0 until n) {
      sum = sum + a(i)

      if (i % 2 == 0) {
        if (sum <= 0) {
          opeCount1 += -sum + 1
          sum = 1
        }
      } else {
        if (sum > 0) {
          opeCount1 += sum + 1
          sum = -1
        }
      }
    }

    sum = 0L
    var opeCount2 = 0L
    // 負、正、負、正（奇数インデックスが正）とする
    for (i <- 0 until n) {
      sum = sum + a(i)

      if (i % 2 != 0) {
        if (sum <= 0) {
          opeCount2 += -sum + 1
          sum = 1
        }
      } else {
        if (sum > 0) {
          opeCount2 += sum + 1
          sum = -1
        }
      }
    }

    println(math.min(opeCount1, opeCount2))
  }


  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    sc.nextLine
    val a = sc.nextLine.split(" ").map(_.toInt).toList

    var prevSum = a(0)
    var opeCount = 0

    for (i <- 1 until n) {
      val currSum = prevSum + a(i)

      if (prevSum < 0 && currSum < 0) {
        opeCount += math.abs(currSum) + 1
        prevSum = 1
      } else if (prevSum > 0 && currSum > 0) {
        opeCount += math.abs(currSum) + 1
        prevSum = -1
      } else {
        if (currSum == 0) {
          opeCount += 1
          if (prevSum < 0) {
            prevSum = 1
          } else {
            prevSum = -1
          }
        } else {
          prevSum = prevSum + a(i)
        }
      }
    }

    println(opeCount)
  }

}