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.Text;
using System.Collections.Generic;
using System.Linq;
class Solve{
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        int N = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        long[] A;
        A = new long[N];
        for(int i=0;i<N;i++){
            A[i] = int.Parse(str[i]);
        }
        long ans;
        long sum = 0;
        long count = 0;
        for(int i=0;i<N;i++){
            sum += A[i];
            if(i % 2 == 0){
                if(sum <= 0){
                    count += 1-sum;
                    sum = 1;
                }
            }
            else{
                if(sum >= 0){
                    count += sum+1;
                    sum = -1;
                }
            }
        }
        ans = count;
        sum = 0;
        count = 0;
        for(int i=0;i<N;i++){
            sum += A[i];
            if(i % 2 != 0){
                if(sum <= 0){
                    count += 1-sum;
                    sum = 1;
                }
            }
            else{
                if(sum >= 0){
                    count += sum+1;
                    sum = -1;
                }
            }
        }
        ans = Math.Min(ans,count);
        sb.Append(ans+"\n");
    }
}