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.Math;

namespace ConsoleApp1
{
    class Program
    {
        static long Solve(long[] A, bool positive)
        {
            long sum = 0, ans = 0;
            foreach (var value in A)
            {
                sum += value;
                if (positive && sum <= 0)
                {
                    long add = 1 - sum;
                    ans += add;
                    sum += add;
                }
                else if (!positive && sum >= 0)
                {
                    long add = sum - (-1);
                    ans += add;
                    sum -= add;
                }

                positive = !positive;
            }

            return ans;
        }

        static void Main(string[] args)
        {
            Console.ReadLine();
            long[] A = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long ans = Min(Solve(A, true), Solve(A, false));
            Console.WriteLine(ans);
        }
    }
}