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;

class Program {
	static void Main(string[] args) {
		new Calc().Solve();
	}
	public class Calc {
		public Calc() { }
		public void Solve() {
			int n = Utils.ReadLine<int>();
			var a = Utils.ReadLine<int>(' ');
			int sum = 0;
			int x = 0, y = 0;
			for (int i = 0; i < n; i++) {
				sum += a[i];
				if (i % 2 == 0) {
					if (sum < 0) continue;
					x += Math.Abs(sum) + 1;
					sum = -1;
				} else {
					if (sum > 0) continue;
					x += Math.Abs(sum) + 1;
					sum = 1;
				}
			}
			sum = 0;
			for (int i = 0; i < n; i++) {
				sum += a[i];
				if (i % 2 == 1) {
					if (sum < 0) continue;
					y += Math.Abs(sum) + 1;
					sum = -1;
				} else {
					if (sum > 0) continue;
					y += Math.Abs(sum) + 1;
					sum = 1;
				}
			}
			Math.Min(x, y).WriteLine();
			return;
		}
	}
}
public static class Utils {
	public static T ReadLine<T>() {
		return (T)Convert.ChangeType(Console.ReadLine(), typeof(T));
	}

	public static T[] ReadLine<T>(params char[] separators) {
		return Console.ReadLine()
			.Split(separators)
			.Where(_ => _.Length > 0)
			.Select(_ => (T)Convert.ChangeType(_, typeof(T)))
			.ToArray();
	}

	public static List<T> ReadLines<T>(int readCount) {
		List<T> rt = new List<T>();
		for (int i = 0; i < readCount; i++) {
			rt.Add(ReadLine<T>());
		}
		return rt;
	}

	public static string Docking<T>(this IEnumerable<T> s, int sequenceRange, Func<T, string> filter = null) {
		string str = "";
		int c = 0;
		foreach (var item in s) {
			str += filter == null ? item.ToString() : filter(item);
			c++;
			if (c == sequenceRange) break;
		}
		return str;
	}

	public static string Docking<T>(this IEnumerable<T> s, Func<T, string> filter = null) {
		return s.Docking(s.Count(), filter);
	}

	public static string RangeDocking<T>(this IEnumerable<T> s, int start, int end, Func<T, string> filter = null) {
		string str = "";
		end = end < s.Count() ? end : s.Count();
		var items = s.ToArray();
		for (int i = start; i < end; i++) {
			str += filter == null ? items[i].ToString() : filter(items[i]);
		}
		return str;
	}
	public static int IntParse(this string n) {
		return int.Parse(n);
	}


	public static void WriteLine(this object obj) {
		Console.WriteLine(obj);
	}
	public static void AddTo<T>(this T obj,List<T> list) {
		list.Add(obj);
	}
}