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 static System.Console;
using static System.Convert;

class Program
{
    static void Main(string[] args)
    {
        var length = ToInt32(ReadLine());
        var result = 0;
        var nums = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var sum = nums[0];
        if (sum == 0) { sum++; result++; }
        var lastSum = sum;
        for(var i = 1; i < length; i++)
        {
            sum += nums[i];
            while (!IsDifferentSign(lastSum, sum)||sum==0)
            {
                if (!IsDifferentSign(lastSum, sum))
                { result += Math.Abs(sum) + 1; sum = lastSum > 0 ? -1 : 1;}
                if (sum == 0) { sum = lastSum > 0 ? --sum : ++sum; result++; }
            }
            lastSum = sum;
        }
        WriteLine(result);
    }

    private static bool IsDifferentSign(int lastSum,int sum)
    {
        return (lastSum > 0 && sum < 0) || (lastSum < 0 && sum > 0);
    }
}