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

class Program{
  public static void Main(){
    
    int n = int.Parse(Console.ReadLine());
    var input = Console.ReadLine().Split();
    int[] a = new int[n];
    for(int i=0; i<n; i++){
      a[i] = int.Parse(input[i]);
    }
    
    long e = 0;
    long o = 0;
    long ewa = 0;
    long owa = 0;
    for(int i=0; i<n; i++){
      ewa += a[i];
      owa += a[i];
      if(i % 2 == 0){
        if(ewa >= 0){
          e += ewa +1;
          ewa = -1;
        }
        if(owa <= 0){
          o += Abs(owa) +1;
          owa = 1;
        }
      }
      else{
        if(ewa <= 0){
          e += Abs(ewa) +1;
          ewa = 1;
        }
        if(owa >= 0){
          o += owa +1;
          owa = -1;
        }
      }
    }
    Console.Write(Min(o,e));
  }
}