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;
namespace ABC059_C{
    class Program{
        static void Main(string[] args){
            var n = long.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            var ans1 = 0L;
            var ans2 = 0L;
            var flag = true;
            var sum = 0L;

            for(var i = 0;i < n;i++){
                sum += a[i];
                if(flag){
                    if(sum <= 0){
                        ans1 += Math.Abs(sum) + 1;
                        sum += Math.Abs(sum) + 1;
                    }
                }else{
                    if(sum >= 0){
                        ans1 += Math.Abs(sum) + 1;
                        sum -= Math.Abs(sum) + 1;
                    }
                }
                flag = (flag) ? false : true;
            }
            sum = 0;
            flag = false;
            for(var i = 0;i < n;i++){
                sum += a[i];
                if(flag){
                    if(sum <= 0){
                        ans2 += Math.Abs(sum) + 1;
                        sum += Math.Abs(sum) + 1;
                    }
                }else{
                    if(sum >= 0){
                        ans2 += Math.Abs(sum) + 1;
                        sum -= Math.Abs(sum) + 1;
                    }
                }
                flag = (flag) ? false : true;
            }

            Console.WriteLine(Math.Min(ans1,ans2));
        }
    }
}