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;

class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        int[] an = Console.ReadLine().Split(' ').Select(e => int.Parse(e)).ToArray();

        long sum = 0;
        long cs1 = 0;
        int t = 1;
        for (int i = 0; i < n; i++)
        {
            sum += an[i];
            if (sum * t <= 0)
            {
                long tmp = Math.Abs(sum - t);
                sum = t;
                cs1 += tmp;
            }
            t *= -1;
        }

        long cs2 = 0;
        t = -1;
        sum = 0;
        for (int i = 0; i < n; i++)
        {
            sum += an[i];
            if (sum * t <= 0)
            {
                long tmp = Math.Abs(sum - t);
                sum = t;
                cs2 += tmp;
            }
            t *= -1;
        }

        Console.WriteLine(Math.Min(cs1, cs2));
    }
}