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

class Program
{
    static void Main(string[] args)
    {
        solve();
    }
    static Scanner cin;
    static int n;
    static int[] a;

    static void input()
    {
        cin = new Scanner();

        n = cin.nextInt();
        a = cin.ArrayInt(n);
    }
    static void solve()
    {
        input();
        int sum = 0;
        long count = 0;
        long ans = 0;
        //even is plus
        for(int i = 0; i < n; i++)
        {
            sum += a[i];
            if(i % 2 == 0 && sum <= 0)
            {
                count += Abs(1 - sum);
                sum = 1;
            }

            if(i % 2 == 1 && sum >= 0)
            {
                count += Abs(-1 - sum);
                sum = -1;
            }
        }
        ans = count;
        sum = 0;
        count = 0;
        for (int i = 0; i < n; i++)
        {
            sum += a[i];
            if (i % 2 == 1 && sum <= 0)
            {
                count += Abs(1 - sum);
                sum = 1;
            }

            if (i % 2 == 0 && sum >= 0)
            {
                count += Abs(-1 - sum);
                sum = -1;
            }
        }
        ans = Min(ans, count);
        WriteLine(ans);
    }
    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }
        
        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }

        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for(int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for(int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }

        public double[] ArrayDounble(int N, int add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }
}