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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class MainClass
{
    static void Main()
    {
        int n = int.Parse(ReadLine());
        var a = ReadLine().Split().Select(long.Parse).ToArray();

        
        long ans = 0;
        long sum = 0;
        bool sign = false;
        for (int i = 0; i < n; i++)
        {
            sum += a[i];
            if (sign && sum <=0)
            {
                ans += Abs(sum) + 1;
                sum = 1;
            }
            else if (!sign && sum >= 0)
            {
                ans += Abs(sum) + 1;
                sum = -1;
            }
            sign = !sign;
        }

        long ans2 = 0;
        sum = 0;
        sign = true;
        for (int i = 0; i < n; i++)
        {
            sum += a[i];
            if (sign && sum <= 0)
            {
                ans2 += Abs(sum) + 1;
                sum = 1;
            }
            else if (!sign && sum >= 0)
            {
                ans2 += Abs(sum) + 1;
                sum = -1;
            }
            sign = !sign;
        }
        WriteLine(Min(ans,ans2));
    }
}