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.InputStream
import java.math.BigDecimal
import java.math.BigInteger

fun main(args: Array<String>) = input.run {
    val n = nextInt()
    val a = nextLongs(n)

    fun solve(sum0: Long): Long {
        var sum = sum0
        var ans = 0L
        (1 until n).forEach {
            if (sum < 0) {
                ans += Math.max(0, 1 - sum - a[it])
                sum = Math.max(1, sum + a[it])
            } else {
                ans += Math.max(0, 1 + sum + a[it])
                sum = Math.min(-1, sum + a[it])
            }
        }
        return ans
    }

    println(Math.min(
        Math.max(0, 1 - a[0]) + solve(Math.max(1, a[0])),
        Math.max(0, 1 + a[0]) + solve(Math.min(-1, a[0]))
    ))
}

val input = FastScanner()

fun String.toBigInteger() = BigInteger(this)
fun String.toBigDecimal() = BigDecimal(this)

class FastScanner(private val input: InputStream = System.`in`) {
    private val sb = StringBuilder()
    private val buffer = ByteArray(4096)
    private var pos = 0
    private var size = 0

    fun nextString(): String? {
        var c = skipWhitespace()
        if (c < 0) return null

        return sb.run {
            setLength(0)

            do {
                append(c.toChar())
                c = read()
            } while (c > ' '.toInt())

            toString()
        }
    }

    fun nextLine(): String? {
        var c = read()
        if (c < 0) return null

        return sb.run {
            setLength(0)

            while (c >= 0 && c != '\n'.toInt()) {
                append(c.toChar())
                c = read()
            }

            toString()
        }
    }

    fun nextLong(): Long {
        var c = skipWhitespace()

        val sign = if (c == '-'.toInt()) {
            c = read()
            -1
        } else 1

        var ans = 0L

        while (c > ' '.toInt()) {
            ans = ans * 10 + c - '0'.toInt()
            c = read()
        }

        return sign * ans
    }

    fun nextInt() = nextLong().toInt()
    fun nextDouble() = nextString()?.toDouble() ?: 0.0
    fun nextBigInteger(): BigInteger = nextString()?.toBigInteger() ?: BigInteger.ZERO
    fun nextBigDecimal(): BigDecimal = nextString()?.toBigDecimal() ?: BigDecimal.ZERO

    fun nextStrings(n: Int) = Array<String>(n) { nextString() ?: "" }
    fun nextInts(n: Int) = IntArray(n) { nextInt() }
    fun nextLongs(n: Int) = LongArray(n) { nextLong() }
    fun nextDoubles(n: Int) = DoubleArray(n) { nextDouble() }
    fun nextBigIntegers(n: Int) = Array<BigInteger>(n) { nextBigInteger() }
    fun nextBigDecimals(n: Int) = Array<BigDecimal>(n) { nextBigDecimal() }

    fun nextStrings(n: Int, m: Int) = Array(n) { nextStrings(m) }
    fun nextInts(n: Int, m: Int) = Array(n) { nextInts(m) }
    fun nextLongs(n: Int, m: Int) = Array(n) { nextLongs(m) }
    fun nextDoubles(n: Int, m: Int) = Array(n) { nextDoubles(m) }
    fun nextBigIntegers(n: Int, m: Int) = Array(n) { nextBigIntegers(m) }
    fun nextBigDecimals(n: Int, m: Int) = Array(n) { nextBigDecimals(m) }

    private fun skipWhitespace(): Int {
        while (true) {
            val c = read()
            if (c > ' '.toInt() || c < 0) return c
        }
    }

    private fun read(): Int {
        while (pos >= size) {
            if (size < 0) return -1
            size = input.read(buffer, 0, buffer.size)
            pos = 0
        }
        return buffer[pos++].toInt()
    }
}