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;
using System.Collections;
using System.Collections.Generic;
using System.Text;


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        var n = long.Parse(Console.ReadLine());
        long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();

        long[] sum = new long[n];
        sum[0] = a[0];
        for (int i = 1; i < n; i++)
        {
            sum[i] = sum[i - 1] + a[i];
        }

        var ans = long.MaxValue;

        //+-+=
        var flag = true;
        long count = 0;
        long tmp = 0;
        for (int i = 0; i < n; i++)
        {
            //前処理
            sum[i] += tmp;

            if (flag)
            {
                //0より大きい数字であることを確認
                if (sum[i] <= 0)
                {
                    tmp += sum[i] * (-1) + 1;
                    count += Math.Abs(sum[i] * (-1) + 1);
                    sum[i] += sum[i] * (-1) + 1;
                }
            }
            else
            {
                //0より小さい数字であることを確認
                if (sum[i] >= 0)
                {
                    tmp += sum[i] * (-1) - 1;
                    count += Math.Abs(sum[i] * (-1) - 1);
                    sum[i] += sum[i] * (-1) - 1;
                }
            }
            flag = !flag;
        }

        ans = Math.Min(ans, count);

        //-+-+
        sum[0] = a[0];
        for (int i = 1; i < n; i++)
        {
            sum[i] = sum[i - 1] + a[i];
        }

        flag = false;
        count = 0;
        tmp = 0;
        for (int i = 0; i < n; i++)
        {
            //前処理
            sum[i] += tmp;

            if (flag)
            {
                //0より大きい数字であることを確認
                if (sum[i] <= 0)
                {
                    tmp += sum[i] * (-1) + 1;
                    count += Math.Abs(sum[i] * (-1) + 1);
                    sum[i] += sum[i] * (-1) + 1;
                }
            }
            else
            {
                //0より小さい数字であることを確認
                if (sum[i] >= 0)
                {
                    tmp += sum[i] * (-1) - 1;
                    count += Math.Abs(sum[i] * (-1) - 1);
                    sum[i] += sum[i] * (-1) - 1;
                }

            }
            flag = !flag;
        }

        ans = Math.Min(ans, count);

        // 出力
        Console.WriteLine(ans);
    }
}