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: Accepted)

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

namespace C
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            var A = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var answer = (long)1e18;
            var t = 1;
            for (var k = 0; k < 2; k++)
            {
                t ^= 1;
                var step = 0L;
                var sum = 0L;
                for (var i = 0; i < N; i++)
                {
                    sum += A[i];

                    if (i % 2 == t)
                    {
                        if (sum <= 0)
                        {
                            step += 1 - sum;
                            sum = 1;
                        }
                    }
                    else
                    {
                        if (sum >= 0)
                        {
                            step += 1 + sum;
                            sum = -1;
                        }
                    }
                }
                answer = Math.Min(answer, step);
            }

            Console.WriteLine(answer);
        }
    }
}