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 java.util.Scanner
 
object Main extends App {
  val sc = new Scanner(System.in)
  System.currentTimeMillis
  val n = sc.nextInt()
  val a = new Array[Int](n)
  for(i <- 0 until n)
    a(i) = sc.nextInt()
 
  var cnt = 0L
  var ans = 0L
  for(i <- 0 until n){
    val now = a(i)
    cnt += now
 
    if(i % 2 == 0){
      if(cnt < 1){
        ans += 1 - cnt
        cnt = 1
      }
    }
    else{
      if(cnt > -1){
        ans += cnt - (-1)
        cnt = -1
      }
    }
  }
 
  cnt = 0L
  var ans2 = 0L
  for(i <- 0 until n){
    val now = a(i)
    cnt += now
 
    if(i % 2 != 0){
      if(cnt < 1){
        ans2 += 1 - cnt
        cnt = 1
      }
    }
    else{
      if(cnt > -1){
        ans2 += cnt - (-1)
        cnt = -1
      }
    }
  }
 
  println(Math.min(ans, ans2))
}