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 (1.3.71) (judge verdict: Accepted)

fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = MyScanner()
        val n = sc.nextInt()
        val a = sc.longList()
        // +-+-+-
        var p = 0L
        var m = 0L
        var tmpP = 0L
        var tmpM = 0L
        for (i in 0 until n) {
            tmpP += a[i]
            tmpM += a[i]
            if (i % 2 == 0) {
                // +
                if (tmpP <= 0) {
                    p += -tmpP + 1
                    tmpP = 1
                }

                if (tmpM >= 0) {
                    m += tmpM + 1
                    tmpM = -1
                }
            } else {
                // -
                if (tmpP >= 0) {
                    p += tmpP + 1
                    tmpP = -1
                }

                if (tmpM <= 0) {
                    m += -tmpM + 1
                    tmpM = 1
                }
            }
        }

        println(Math.min(p,m))
    }
}

class MyScanner {
    private var ptr = 0
    private var l = listOf<String>()

    fun next(): String {
        while (l.size <= ptr) {
            l = readLine()!!.split(' ')
            ptr = 0
        }
        return l[ptr++]
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextDouble() = next().toDouble()
    fun nextCharArray() = next().toCharArray()
    fun nextChar() = next()[0]

    fun list(): List<String> {
        ptr = l.size
        return readLine()!!.split(' ')
    }

    fun intList() = list().map { s -> s.toInt() }
    fun longList() = list().map { s -> s.toLong() }
    fun doubleList() = list().map { s -> s.toDouble() }

    fun array() = list().toTypedArray()
    fun intArray() = intList().toIntArray()
    fun longArray() = longList().toLongArray()
    fun doubleArray() = doubleList().toDoubleArray()
}