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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.InputStreamReader
import java.io.BufferedReader

fun main(args: Array<String>) {
  val br = BufferedReader(InputStreamReader(System.`in`))

  br.readLine()
  val a = br.readLine().split(" ").map { it.toLong() }
    .toLongArray()

  fun solve(init: Int): Long {
    return a.foldIndexed(Pair(0L,0L)) { i, acc, e ->
      val v = acc.second + e
      // println("${i}: ${acc}, ${v}")
      if(i % 2 == init) {
        if(v > 0) Pair(acc.first, v)
        else Pair(acc.first - v + 1L, 1L)
      }
      else {
        if(v < 0) Pair(acc.first, v)
        else Pair(acc.first + v + 1L, -1L)
      }
    }.first
  }

  val ans = Math.min(solve(0), solve(1))
  println(ans)
}