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;

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        string[] line = Console.ReadLine().Trim().Split(' ');
        var a = Array.ConvertAll(line, long.Parse);
        var ret0 = culc0m(a);
        var ret1 = culc0p(a ,ret0);
        if (ret1 == -1) Console.WriteLine(ret0);
        else   Console.WriteLine(Math.Min(ret0,ret1));
    }
    public static long culc0m(long[] a)
    {
        var count = 0L;
        var sum = a[0];
        if (sum >= 0) { count += sum + 1; sum = -1; }
        for (int i = 1; i < a.Length; i++)
        {
            if (i % 2 == 1)
            {
                if (sum + a[i] > 0) sum += a[i];
                else { count += -(sum + a[i]) + 1; sum = 1; }
            }
            else
            {
                if (sum + a[i] < 0) sum += a[i];
                else { count += (sum + a[i]) + 1; sum = -1; }
            }
        }
        return count;
    }
    public static long culc0p(long[] a, long b)
    {
        var count = 0L;
        var sum = a[0];
        if (sum <= 0) { count += -sum + 1; sum = 1; }
        for (int i = 1; i < a.Length; i++)
        {
            if (i % 2 == 1)
            {
                if (sum + a[i] < 0) sum += a[i];
                else { count += (sum + a[i]) + 1; sum = -1; }
            }
            else
            {
                if (sum + a[i] > 0) sum += a[i];
                else { count += -(sum + a[i]) + 1; sum = 1; }
            }
            if (count > b) return -1;
        }
        return count;
    }
}