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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var N = Sarray()[0];
            var Ai = Sarray();
            //+から
            var ansp = 0L;
            var ansm = 0L;
            var sump = 0L;
            var summ = 0L;
            for (var i = 0; i < N; ++i)
            {
                sump += Ai[i];
                summ += Ai[i];
                if (i % 2 == 0)
                {
                    if (sump < 1)
                    {
                        ansp += -sump + 1;
                        sump = 1;
                    }
                    if (-1 < summ)
                    {
                        ansm += summ + 1;
                        summ = -1;
                    }
                }
                else
                {
                    if (-1 < sump)
                    {
                        ansp += sump + 1;
                        sump = -1;
                    }
                    if (summ < 1)
                    {
                        ansm += -summ + 1;
                        summ = 1;
                    }
                }
            }
            WriteLine(Min(ansp, ansm));
            //Out.Flush();
        }
    }
}