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;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
using static CS_Contest.Utils;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
	class Program {
        static void Main(string[] args) {
			new Calc().Solve();
			return;
        }

		private class Calc {
			public void Solve() {
				int N = ReadInt();
				var a = ReadInt(' ');
				int cnt = 0;
				int sum = a[0];
				foreach (var item in a.Select((x,i)=>new { X = x, I = i }).Where(x=>x.I>=1).Select(x=>x.X)) {
					var asum = sum + item;
					if (asum * sum < 0) { sum += item;continue; }

					cnt += Abs(asum) + 1;
					sum = sum<0?1:-1;
				}
				cnt.WL();
				return;
			}
		}
    }

	
	
    public static class Utils {
		public static int INF = (int)(1e9);
        public static void WL(this object obj) => WriteLine(obj);
        public static void WL(this string obj) => WriteLine(obj);
        public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());
		public static int ReadInt() => int.Parse(ReadLine());
		public static List<int> ReadInt(char s) => ReadLine().Split(s).Select(int.Parse).ToList();
		public static long ReadLong() => long.Parse(ReadLine());
		public static List<long> ReadLong(char s) => ReadLine().Split(s).Select(long.Parse).ToList();
		public static void REP(int n,Action<int> act) {
			for (int i = 0; i < n; i++) {
				act(i);
			}
		}
		public static void RREP(int n,Action<int> act) {
			for (int i = n-1; i >=0; i--) {
				act(i);
			}
		}
		public static void REP(long n, Action<int> act) => REP((int)n, act);
		public static void RREP(long n, Action<int> act) => RREP((int)n, act);

		public static void Yes() => "Yes".WL();
		public static void No() => "No".WL();
		public static void YES() => "YES".WL();
		public static void NO() => "NO".WL();


		public static int ManhattanDistance(int x1, int y1, int x2, int y2) => Abs(x2 - x1) + Abs(y2 - y1);

		public class Tree {
			public LLi Graph;
			public Tree(int nodes) {
				Graph = new LLi();
				REP(nodes, x => {
					Graph.Add(new Li());
				});
			}
			public void Add(int x,int y) {
				Graph[x].Add(y);
				Graph[y].Add(x);
			}
		}
    }
}