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;

namespace ABC059_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var a = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            var ans1 = 0L;
            var ans2 = 0L;
            var sum1 = 0L;
            var sum2 = 0L;
            for (var i=0;i<n;i++)
            {
                sum1 += a[i];
                if(i%2 == 0)
                {
                    if(sum1<=0)
                    {
                        ans1 += Math.Abs(sum1) + 1;
                        sum1 = 1;
                    }
                }
                else
                {
                    if(sum1>=0)
                    {
                        ans1 += sum1 + 1;
                        sum1 = -1;
                    }
                }
            }
            for(var i=0;i<n;i++)
            {
                sum2 += a[i];
                if (i % 2 == 0)
                {
                    if (sum2 >= 0)
                    {
                        ans2 += sum2 + 1;
                        sum2 = -1;
                    }
                }
                else
                {
                    if (sum2 <= 0)
                    {
                        ans2 += Math.Abs(sum2) + 1;
                        sum2 = 1;
                    }
                }
            }
            var ans = Math.Min(ans1, ans2);
            Console.WriteLine(ans);
        }
    }
}