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: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.nextInt()
    val a = (0 until n).map { sc.next().toLong() }
    println(problem059c(n, a))
}

fun problem059c(n: Int, a: List<Long>): Long {
    val count1 = compute(n, a)
    val a = a.toMutableList()
    var a0 = a[0]
    var count = 0L
    if (a0 > 0) {
        val tmp = a0 + 1
        a[0] = a0 - tmp
        count += tmp
    } else {
        val tmp = a0 - 1
        a[0] = a0 - tmp
        count -= tmp
    }
    val count2 = compute(n, a) + count
    return Math.min(count1, count2)
}

fun compute(n: Int, a: List<Long>): Long {
    val a = a.toMutableList()
    var count = 0L
    for (i in 0 until n) {
        val ai = a[i]
        val sum = a.take(i).sum() + ai
        if (sum == 0L) {
            break
        }
        if (i >= n - 1) {
            continue
        }
        val sum2 = sum + a[i + 1]
        if (sum * sum2 < 0) {
            continue
        } else {
            if (sum > 0) {
                val tmp = sum2 + 1
                a[i + 1] = sum2 - tmp
                count += tmp
            } else {
                val tmp = sum2 - 1
                a[i + 1] = sum2 - tmp
                count -= tmp
            }
        }
    }
    return count
}