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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = ReadInt();
            var a = ReadArrayInt();
            var plus = 0L;
            var val = 0L;
            for (int i = 0; i < n; i++)
            {
                val += a[i];
                if (i % 2 == 0)
                {
                    if (val <= 0)
                    {
                        plus += Math.Abs(val) + 1;
                        val = 1;
                    }
                }
                else
                {
                    if (val >= 0)
                    {
                        plus += Math.Abs(val) + 1;
                        val = -1;
                    }
                }
            }
            var minus = 0L;
            val = 0;
            for (int i = 0; i < n; i++)
            {
                val += a[i];
                if (i % 2 != 0)
                {
                    if (val <= 0)
                    {
                        minus += Math.Abs(val) + 1;
                        val = 1;
                    }
                }
                else
                {
                    if (val >= 0)
                    {
                        minus += Math.Abs(val) + 1;
                        val = -1;
                    }
                }
            }

            Console.WriteLine(plus < minus ? plus : minus);
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}