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;
using System.Text;

namespace ARC072
{
    public class C
    {
        private long[] A;

        private long F(bool positive)
        {
            long result = 0;

            long current = A[0];

            if (current == 0)
            {
                result += 1;
                current = (positive ? 1 : -1);
            }

            bool nextUp = (current < 0);

            foreach (var a in A.Skip(1))
            {
                current += a;
                if (nextUp)
                {
                    if (current <= 0)
                    {
                        result += (-current + 1);
                        current = 1;
                    }
                }
                else
                {
                    if (current >= 0)
                    {
                        result += (current + 1);
                        current = -1;
                    }
                }
                nextUp ^= true;
            }

            return result;
        }

        private void Run()
        {
            var n = int.Parse(Console.ReadLine().Trim());
            A = Console.ReadLine().Trim().Split().Select(long.Parse).ToArray();
            Console.WriteLine(Math.Min(F(true), F(false)));
        }

        public static void Main()
        {
            var old = Console.Out;
            using (var writer = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Console.SetOut(writer);
                new C().Run();
                Console.Out.Flush();
                Console.SetOut(old);
            }
        }
    }
}