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: Time Limit Exceeded)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCorder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var n = cin.ReadInt;
            var a = cin.ReadLongArray(n);
            var ans = 0L;
            for(int i = 1; i < n; i++)
            {
                var pre = (long)a.Take(i).Sum();
                var now = (long)a.Take(i + 1).Sum();
                if(pre * now < 0)
                {
                    continue;
                }
                if(now > 0)
                {
                    ans += a[i] + (pre + 1);
                    a[i] = -1 * (pre + 1);
                }
                else
                {
                    ans += -1 * (pre - 1) - a[i];
                    a[i] = -1 * (pre - 1);
                }
            }
            WriteLine(ans);
        }



        public long C(int X, int Y)
        {

            if (Y == 0 || Y == X)
            {
                return 1;
            }
            if (X < Y)
            {
                return 0;
            }
            var Pascal = new long[X + 1, X + 1];
            for (int i = 0; i <= X; i++)
            {
                Pascal[i, 0] = 1L;
                Pascal[i, i] = 1L;
            }
            for (int i = 2; i <= X; i++)
            {
                for (int j = 1; j < i; j++)
                {
                    Pascal[i, j] = Pascal[i - 1, j] + Pascal[i - 1, j - 1];
                }
            }
            return Pascal[X, Y];
        }

        public class ConsoleInput
        {
            private readonly System.IO.TextReader _stream;
            private char _separator = ' ';
            private Queue<string> inputStream;
            public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
            {
                this._separator = separator;
                this._stream = stream;
                inputStream = new Queue<string>();
            }
            public string Read
            {
                get
                {
                    if (inputStream.Count != 0) return inputStream.Dequeue();
                    string[] tmp = _stream.ReadLine().Split(_separator);
                    for (int i = 0; i < tmp.Length; ++i)
                        inputStream.Enqueue(tmp[i]);
                    return inputStream.Dequeue();
                }
            }
            public string ReadLine { get { return _stream.ReadLine(); } }
            public int ReadInt { get { return int.Parse(Read); } }
            public long ReadLong { get { return long.Parse(Read); } }
            public double ReadDouble { get { return double.Parse(Read); } }
            public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
            public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
            public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        }
    }
}