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.*
import java.util.*

fun solve(n: Int, a: LongArray){
    var ans1 = 0L
    var ret1 = 0L
    var ans2 = 0L
    var ret2 = 0L
    for(i in 0 until n){
        ret1 += a[i]
        ret2 += a[i]
        if(i % 2 == 0 && ret1 <= 0){
            ans1 -= ret1 - 1
            ret1 = 1L
        }else if(i % 2 == 1 && ret1 >= 0){
            ans1 += ret1 + 1
            ret1 = -1L
        }
        if(i % 2 == 0 && ret2 >=0){
            ans2 += ret2 + 1
            ret2 = -1L
        }else if(i % 2 == 1 && ret2 <= 0){
            ans2 -= ret2 - 1
            ret2 = 1L
        }
    }
    println(Math.min(ans1, ans2))
    return
}


fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val n = sc.next().toInt()
    val a = LongArray(n)
    for (i in 0 until n) {
        a[i] = sc.next().toLong()
    }
    solve(n, a)
}