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: Accepted)

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

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var n = long.Parse(Console.ReadLine());
			var aList = Console.ReadLine().Split(' ').Select(value => long.Parse(value)).ToList();

			if (aList[0] == 0)
			{
				var min = long.MaxValue;
				aList[0] = 1;
				min = Math.Min(Sequence(aList), min);
				aList[0] = -1;
				min = Math.Min(Sequence(aList), min);

				Console.WriteLine(min + 1);
			}
			else
			{
				var min = long.MaxValue;
				min = Math.Min(Sequence(aList), min);

				long tmp;
				if(aList[0] > 0)
				{
					tmp = aList[0] + 1;
					aList[0] = -1;
				}
				else
				{
					tmp = -aList[0] + 1;
					aList[0] = 1;
				}
				min = Math.Min(Sequence(aList) + tmp, min);

				Console.WriteLine(min);
			}
		}

		private static long Sequence(List<long> list)
		{
			long sum = list[0];
			var isPreviousSumPositive = list[0] > 0;
			long count = 0;

			for (var i = 1; i < list.Count; i++)
			{
				sum += list[i];
				if (isPreviousSumPositive && sum >= 0)
				{
					count += sum + 1;
					sum = -1;
				}
				else if (!isPreviousSumPositive && sum <= 0)
				{
					count += -sum + 1;
					sum = 1;
				}

				if (sum > 0)
				{
					isPreviousSumPositive = true;
				}
				else
				{
					isPreviousSumPositive = false;
				}
			}

			return count;
		}
	}
}