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)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val aList = readLine()!!.split(' ').map(String::toLong)
    println(Math.min(calcCount(aList,true),calcCount(aList,false)))
}

fun calcCount(aList: List<Long>, f:Boolean): Long {
    var flag = f
    var sum = 0L
    var count = 0L

    for (i in 0 until aList.size) {
        sum += aList[i]
        when {
            sum == 0L -> {
                count++
                sum = if (flag) 1 else -1
            }
            flag == sum > 0 -> {
                //do nothing
            }
            flag == sum < 0 -> {
                count += Math.abs(sum) + 1
                sum = if (flag) 1 else -1
            }
        }
        flag = !flag
    }
    return count
}