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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

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

namespace ProgramingStydying
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(int.Parse).ToList();

            var ans = 0;

            if(a[0] == 0)
            {
                ans = Math.Min(Solve(n, a, 1), Solve(n, a, -1)) + 1;    
            }
            else if(a[0] > 0)
            {
                ans = Math.Min(Solve(n, a, a[0]), Solve(n, a, -1) + a[0] + 1);
            }
            else
            {
                ans = Math.Min(Solve(n, a, a[0]), Solve(n, a, 1) - a[0] + 1);
            }

            Console.WriteLine(ans);
        }

        static int Solve(int n, List<int> a, int sum)
        {
            var ans = 0;

            for (int i = 1; i < n; i++)
            {
                if (sum > 0)
                {
                    sum += a[i];
                    if (sum < 0)
                    {
                        continue;
                    }
                    else
                    {
                        ans += sum + 1;
                        sum = -1;
                    }
                }
                else if (sum < 0)
                {
                    sum += a[i];
                    if (sum > 0)
                    {
                        continue;
                    }
                    else
                    {
                        ans += -sum + 1;
                        sum = 1;
                    }
                }
            }
            return ans;
        }
    }
}