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.Text;

namespace AtTest.C_Challenge
{
    class ABC_059
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] input = Console.ReadLine().Split(' ');
            var array = new long[n];
            for (int i = 0; i < n; i++)
            {
                array[i] = long.Parse(input[i]);
            }

            long sum = 0;
            bool plus = true;
            long firstPlusCnt = 0;
            for(int i = 0; i < n; i++)
            {
                sum += array[i];
                if (plus && sum <= 0)
                {
                    firstPlusCnt += 1-sum;
                    sum = 1;
                }
                else if (!plus && 0 <= sum)
                {
                    firstPlusCnt += 1 + sum;
                    sum = -1;
                }
                plus = !plus;
            }

            sum = 0;
            plus = false;
            long firstMinusCnt = 0;
            for (int i = 0; i < n; i++)
            {
                sum += array[i];
                if (plus && sum <= 0)
                {
                    firstMinusCnt += 1-sum;
                    sum = 1;
                }
                else if (!plus && 0 <= sum)
                {
                    firstMinusCnt += 1 + sum;
                    sum = -1;
                }
                plus = !plus;
            }

            if (firstPlusCnt < firstMinusCnt)
            {
                Console.WriteLine(firstPlusCnt);
            }
            else
            {
                Console.WriteLine(firstMinusCnt);
            }
        }
    }
}