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 static System.Convert;
using static System.Console;
using static System.Math;
class MainClass
{
	static void Main(string[] args)
	{
		{
			string n = ReadLine();
			int[] arr = ReadLine().Split(' ').Select(int.Parse).ToArray();
			WriteLine(Min(GetCnt(arr, true), GetCnt(arr, false)));
		}
    }
    private static long GetCnt(int[] arr,bool isPlus)
          {
              var result = 0L;
              var sum = 0L;
              for(int i = 0; i < arr.Length; i++)
              {
                  sum += arr[i];
                  if (isPlus)
                  {
                      if (sum <= 0) { result += 1 - sum;sum = 1; }
                  }
                  else
                      if (sum >= 0) { result += 1 + sum;sum = -1; }
                  isPlus = isPlus ? false : true;
              }
              return result;
		}
}