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.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
	return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
}

class Program
{
    public static void Main()
    {
	int n = int.Parse(ReadLine());
	int[] a = ReadIntArray();

	long[] s = new long[n];
	s[0] = a[0];
	for (int i = 1; i < n; i++)
	{
	    s[i] = s[i-1] + a[i];
	}
		 
	// ty1: +-+-..., ty2: -+-+...
	long n1 = 0, n2 = 0;
	long offset1 = 0, offset2 = 0;

	for (int i = 0; i < n; i++)
	{
	    long gap1 = 0, gap2 = 0;
	    if ((i&1) == 0)
	    {
		if (s[i] + offset1 <= 0)
		{
		    gap1 =  1 - (s[i] + offset1);
		}

		if (s[i] + offset2 >= 0)
		{
		    gap2 = -1 - (s[i] + offset2);
		}
	    }
	    else
	    {
		if (s[i] + offset1 >= 0)
		{
		    gap1 =  -1 - (s[i] + offset1);
		}

		if (s[i] + offset2 <= 0)
		{
		    gap2 = 1 - (s[i] + offset2);
		}
	    }
	    n1 += Math.Abs(gap1);
	    offset1 += gap1;
	    n2 += Math.Abs(gap2);
	    offset2 += gap2;
	}
	WriteLine(Math.Min(n1, n2));
    }
}