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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

namespace ABC059C
{
    class Program
    {
        // -1 4 3  2 -5 4
        // -1 4 -4 2 -5 5 -> 8
        static long sequentialize(int[] a, bool firstPlus)
        {
            var n = a.Length;
            var changeCount = 0L;

            if (firstPlus && a[0] <= 0)
            {
                changeCount += 1 - a[0];
                a[0] = 1;
            }
            else if (!firstPlus && a[0] >= 0)
            {
                changeCount += 1 + a[0];
                a[0] = -1;
            }

            var sum = a[0];
            int v = a[0] > 0 ? 1 : -1;

            for (int i = 1; i < n; i++)
            {
                var temp = sum + a[i];

                if (sum > 0 && temp > 0)
                {
                    // tempを-1にしたい
                    var prev = a[i];
                    a[i] = -sum - 1;
                    changeCount += Math.Abs(prev - a[i]);
                }
                else if (sum < 0 && temp < 0)
                {
                    // tempを+1にしたい
                    var prev = a[i];
                    a[i] = -sum + 1;
                    changeCount += Math.Abs(prev - a[i]);
                }
                else if (temp == 0)
                {
                    changeCount += 1;
                    a[i] = v;
                }

                sum += a[i];
                v = -v;
            }

            return changeCount;
        }

        static void Solve()
        {
            var n = Input.NextInt();
            var a = Input.NextInt(n).ToArray();
            var b = new int[n];

            a.CopyTo(b, 0);

            var changeCount1 = sequentialize(a, true);
            var changeCount2 = sequentialize(b, false);

            Console.WriteLine(Math.Min(changeCount1, changeCount2));
        }

        #region Competitive Template
        public static void Main(string[] args)
        {
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 仮想的に標準入力をセットする
            // NextLine系を使っていると使えない
            //var sr = new System.IO.StreamReader(@"..\..\input.txt");
            //Input.SetText(sr.ReadToEnd());

            Solve();

            Console.Out.Flush();
        }

        static class Input
        {
            static char[] separator = { ' ', '\r', '\n' };
            public static bool IsEof { get; set; }
            static Queue<string> q { get; set; }

            static Input()
            {
                IsEof = false;
                q = new Queue<string>();
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public static void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public static bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            static bool read()
            {
                var s = Console.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public static string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        IsEof = true;
                        return "";
                    }
                }

                return q.Dequeue();
            }

            public static int NextInt() => int.Parse(Next());
            public static long NextLong() => long.Parse(Next());
            public static double NextDouble() => double.Parse(Next());

            public static List<string> Next(int n) => Enumerable.Range(0, n).Select(_ => Next()).ToList();
            public static List<int> NextInt(int n) => Next(n).Select(x => int.Parse(x)).ToList();
            public static List<long> NextLong(int n) => Next(n).Select(x => long.Parse(x)).ToList();
            public static List<double> NextDouble(int n) => Next(n).Select(x => double.Parse(x)).ToList();

            public static List<string> NextLine() => Console.ReadLine().Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries).ToList();
            public static List<int> NextIntLine() => NextLine().Select(x => int.Parse(x)).ToList();
            public static List<long> NextLongLine() => NextLine().Select(x => long.Parse(x)).ToList();
            public static List<double> NextDoubleLine() => NextLine().Select(x => double.Parse(x)).ToList();
        }
        #endregion
    }
}