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.Generic;
using System.Linq;
using static AtCoder.Io;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var n = ReadInt();
            var a = ReadIntArray();

            var count = new long[] { 0, 0 };

            for (int i = 0; i < count.Length; i++)
            {
                long sum = 0;
                var isPositive = i == 0;

                for (int j = 0; j < a.Length; j++)
                {
                    isPositive = !isPositive;
                    if (sum + a[j] >= 0 && !isPositive)
                    {
                        var diff = -1 - (sum + a[j]);
                        count[i] += Math.Abs(diff);
                        sum += a[j] + diff;
                    }
                    else if (sum + a[j] <= 0 && isPositive)
                    {
                        var diff = 1 - (sum + a[j]);
                        count[i] += Math.Abs(diff);
                        sum += a[j] + diff;
                        
                    }
                    else
                    {
                        sum += a[j];
                    }
                }
            }

            Console.WriteLine($"{count.Min()}");
        }
    }

    public static class Io
    {
        public static string ReadString() => Console.ReadLine();
        public static string[] ReadStringArray() => ReadString().Split(' ');
        public static int ReadInt() => int.Parse(ReadString());
        public static long ReadLong() => long.Parse(ReadString());
        public static int[] ReadIntArray() => ReadStringArray().ParseInt().ToArray();
        public static long[] ReadLongArray() => ReadStringArray().ParseLong().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(int.Parse);
        public static IEnumerable<long> ParseLong(this IEnumerable<string> source) => source.Select(long.Parse);
    }
}