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;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static long Solve(int n, long[] A)
        {
            long sum1 = 0;
            long sum2 = 0;
            long res1 = 0;
            long res2 = 0;
            for (int i = 0; i < n; ++i)
            {
                sum1 += A[i];
                sum2 += A[i];
                if (i % 2 == 0)
                {
                    if (sum1 >= 0)
                    {
                        res1 += sum1 + 1;
                        sum1 = -1;
                    }
                    if (sum2 <= 0)
                    {
                        res2 += -sum2 + 1;
                        sum2 = 1;
                    }
                }
                else
                {
                    if (sum1 <= 0)
                    {
                        res1 += -sum1 + 1;
                        sum1 = 1;
                    }
                    if (sum2 >= 0)
                    {
                        res2 += sum2 + 1;
                        sum2 = -1;
                    }
                }
            }
            return Math.Min(res1, res2);
        }
        static void Main(string[] args)
        {
            int n = ReadInt();
            long[] A = ReadLongs();
            Console.WriteLine(Solve(n, A));
        }
    }
}