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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			long[] a = cin.ArrayLong(n);

			{
				bool ok = true;
				long sum = 0;
				for (int i = 0; i < n; i++) {
					long next = sum + a[i];
					if (next == 0 || sum * next >= 0) {
						ok = false;
						break;
					}

					sum = next;
				}

				if (ok) {
					Console.WriteLine(0);
					return;
				}
			}

			long ans1 = 0;
			{
				long current = a[0];
				if (current <= 0) {
					current = 1;
					ans1 += Math.Abs(a[0]) + 1;
				}
				for (int i = 1; i < n; i++) {
					long next = current + a[i];
					if (current * next < 0) {
						current = next;
						continue;
					}

					long temp = current * a[i];
					if (temp > 0) {
						ans1 += Math.Abs(a[i]) + Math.Abs(current) + 1;
						current = current > 0 ? -1 : 1;
					} else if (temp < 0) {
						ans1 += Math.Abs(current + a[i]) + 1;
						current = current > 0 ? -1 : 1;
					} else {
						ans1 += Math.Abs(current) + 1;
						current = current > 0 ? -1 : 1;
					}
				}
			}

			long ans2 = 0;
			{
				long current = a[0];
				if (current >= 0) {
					current = -1;
					ans2 += Math.Abs(a[0]) + 1;
				}
				for (int i = 1; i < n; i++) {
					long next = current + a[i];
					if (current * next < 0) {
						current = next;
						continue;
					}

					long temp = current * a[i];
					if (temp > 0) {
						ans2 += Math.Abs(a[i]) + Math.Abs(current) + 1;
						current = current > 0 ? -1 : 1;
					} else if (temp < 0) {
						ans2 += Math.Abs(current + a[i]) + 1;
						current = current > 0 ? -1 : 1;
					} else {
						ans2 += Math.Abs(current) + 1;
						current = current > 0 ? -1 : 1;
					}
				}
			}

			Console.WriteLine(Math.Min(ans1, ans2));
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private string[] buf_;
		private int index_;
		Func<string> reader_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}