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 System.Text;
using System.Threading.Tasks;

namespace ABC_C
{
    class C059
    {
        static void Main(string[] args)
        {
            string[] s1 = Console.ReadLine().Split(' ');
            int n = int.Parse(s1[0]);
            string[] a= Console.ReadLine().Split(' ');

            long counter1 = 0, counter2 = 0;
            long[] S1 = new long[n+1]; //0+-+-+-
            long[] S2 = new long[n+1]; //0-+-+-+
            for (int i = 1; i <= n; i++)
            {
                long x = long.Parse(a[i-1]);
                long x1 = x, x2 = x;
                long n1 = S1[i - 1] + x;
                long n2 = S2[i - 1] + x;

                if (i % 2 == 0)
                {
                    if (n1 >= 0)
                    {
                        counter1 += n1 + 1;
                        x1 -= (n1 + 1);
                    }
                    if (n2 <= 0)
                    {
                        counter2 += -n2 + 1;
                        x2 += (-n2 + 1);
                    }
                }
                else
                {
                    if (n1 <= 0)
                    {
                        counter1 += -n1 + 1;
                        x1 += (-n1 + 1);
                    }
                    if (n2 >= 0)
                    {
                        counter2 += n2 + 1;
                        x2 -= (n2 + 1);
                    }
                }
                S1[i] = S1[i - 1] + x1;
                S2[i] = S2[i - 1] + x2;
            }

            long c = Math.Min(counter1, counter2);
            Console.WriteLine(c);
        }
    }
}