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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("4");
            WillReturn.Add("1 -3 1 0");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5");
            WillReturn.Add("3 -6 4 -5 7");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("6");
            WillReturn.Add("-1 4 3 2 -5 4");
            //8
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] AArr = InputList[1].Split(' ').Select(X => int.Parse(X)).ToArray();

        if (AArr[0] == 0) {
            AArr[0] = 1;
            long Cost1 = Solve(AArr) + 1;
            AArr[0] = -1;
            long Cost2 = Solve(AArr) + 1;
            Console.WriteLine(Math.Min(Cost1, Cost2));
        }
        else {
            Console.WriteLine(Solve(AArr));
        }
    }

    static long Solve(int[] pArr)
    {
        long Cost = 0;
        long RunSum = pArr[0];

        for (int I = 1; I <= pArr.GetUpperBound(0); I++) {
            if (RunSum < 0) {
                RunSum += pArr[I];
                if (RunSum > 0) continue;
                Cost += Math.Abs(RunSum) + 1;
                RunSum = 1;
            }
            else if (RunSum > 0) {
                RunSum += pArr[I];
                if (RunSum < 0) continue;
                Cost += Math.Abs(RunSum) + 1;
                RunSum = -1;
            }
        }
        return Cost;
    }
}