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 System.Text;
using System.Collections.Generic;
using System.Linq;
 
class Program {
    static List<long> rep;
    static void Main(string[] args){
        //入力を受け取る
        var N = long.Parse(Console.ReadLine());
        var A  = Console.ReadLine().Split().Select(a => long.Parse(a)).ToArray();
        var B = A;
        long ans = 0;
        long sum = A[0];
        for(int i =1 ;i <N; i++){
            if(sum > 0){
                if(sum+A[i] >= 0){
                    var aim = sum*(-1)-1;
                    ans += (long) Math.Abs(A[i]-aim);
                    A[i] = aim;
                }
            }else{
                if(sum+A[i] <= 0){
                    var aim = sum*(-1)+1;
                    ans += (long) Math.Abs(A[i]-aim);
                    A[i] = aim;
                }
            }
            sum += A[i];
        }
        
        long ans2 = (long)Math.Abs(B[0])+1;
        long sum2 = 0;
        if(B[0] > 0){
          sum2 = -1;
        }else{
          sum2 = 1;
        }
        for(int i =1 ;i <N; i++){
            if(sum2 > 0){
                if(sum2+B[i] >= 0){
                    var aim = sum2*(-1)-1;
                    ans2 += (long) Math.Abs(B[i]-aim);
                    B[i] = aim;
                }
            }else{
                if(sum2+B[i] <= 0){
                    var aim = sum2*(-1)+1;
                    ans2 += (long) Math.Abs(B[i]-aim);
                    B[i] = aim;
                }
            }
            sum2 += B[i];
        }
      
        if(ans2 < ans){
          Console.WriteLine(ans2);
        }else{
          Console.WriteLine(ans);
        }
       　
        
        
    }
    
 
}