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: Time Limit Exceeded)

using System;
using System.Linq;

namespace A
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var aList = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            var total = 0;
            var count = 0;
            foreach (var a in aList)
            {
                var preTotal = total;
                total += a;

                while (preTotal > 0 && total >= 0)
                {
                    total--;
                    count++;
                }

                while (preTotal < 0 && total <= 0)
                {
                    total++;
                    count++;
                }
            }

            Console.WriteLine(count);
        }

        static int NumberOfDigits(long x)
        {
            if (x < 10) return 1;

            var result = 0;
            while (x > 0)
            {
                result++;
                x /= 10;
            }

            return result;
        }

        static int SumOfDigits(int x)
        {
            var sum = 0;
            while (x > 0)
            {
                sum += x % 10;
                x /= 10;
            }

            return sum;
        }
    }
}