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: Wrong Answer)

using System;
using static System.Console;
using static System.Math;

public class Hello{
    public static void Main(){
        int kazu = int.Parse(ReadLine());
        string[] number = ReadLine().Split(' ');
        long wa = 0;
        long wa2 = 0;
        int num0 = int.Parse(number[0]);
        long count = 0;
        long ans =0;
        if(num0 == 0){
            wa = 1;
            wa2 = -1;
            count++;
        }else{
            wa = num0;
        }
        for(int i=1;i<kazu;i++){
            int numi = int.Parse(number[i]);
            long temp = wa + numi;
            if(wa > 0){
                if(temp < 0){
                    wa = temp;
                }else{
                    count += Abs(numi + wa) + 1;
                    wa = -1;
                }
            }else if(wa < 0){
                if(temp > 0){
                    wa = temp;
                }else{
                    count += Abs(numi + wa) + 1;
                    wa = 1;
                }
            }
        }
        ans = count;
        
        if(wa2 != 0){
            count = 1;
        for(int i=1;i<kazu;i++){
            int numi = int.Parse(number[i]);
            long temp = wa2 + numi;
            if(wa2 > 0){
                if(temp < 0){
                    wa2 = temp;
                }else{
                    count += Abs(numi + wa2) + 1;
                    wa2 = -1;
                }
            }else if(wa2 < 0){
                if(temp > 0){
                    wa2 = temp;
                }else{
                    count += Abs(numi + wa2) + 1;
                    wa2 = 1;
                }
            }
        }
        }
        WriteLine(Min(count,ans));
    }
}