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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.Arrays;

public class Main{
  static int n;
  static long[] a;

  static final boolean DEBUG = false;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    n = sc.nextInt();
    a = new long[n];
    for(int i = 0; i < n; i++){
      a[i] = sc.nextInt();
    }

    long count = 0, count2 = 0;
    long sum = a[0];
    long sum2 = a[0] < 0 ? 1 : -1;
    count2 = Math.abs(sum2 - a[0]);
    for(int i = 1; i < n; i++){
      long val = a[i], val2 = a[i];
      if(!((sum > 0 && sum + a[i] < 0) || 
            (sum < 0 && sum + a[i] > 0))){
        val = -sum + ((sum < 0) ? 1 : -1);
        count += Math.abs(val - a[i]);
      }
      if(!((sum2 > 0 && sum2 + a[i] < 0) || 
            (sum2 < 0 && sum2 + a[i] > 0))){
        val2 = -sum2 + ((sum2 < 0) ? 1 : -1);
        count2 += Math.abs(val2 - a[i]);
      }
      sum += val;
      sum2 += val2;
    }

    if(DEBUG){
      System.out.println(Arrays.toString(a));
    }

    System.out.println(Math.min(count, count2));
  }
}