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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
  public static void main (String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.next());
    long[] a = new long[n+1];
    long[] b = new long[n+1];
    long ans1 =0, ans2 =0,total =0;
    
    //a[1]を+とするケース
    for (int i =1; i<=n; i++) {
      a[i] = Long.parseLong(sc.next());
      b[i] = a[i];
      total += a[i];
      if (i % 2 == 1 && total <=0) {
        ans1 += 1 - (total);
        a[i] += ans1;
        total += ans1;
      }
      if (i % 2 == 0 && total >=0) {
        ans1 += 1 + total;
        a[i] += -ans1;
        total += -ans1;
      }
    }
    
    total =0;
    
     //a[1]を-とするケース
    for (int i =1; i<=n; i++) {
      total += b[i];
      if (i % 2 == 0 && total <=0) {
        ans2 += 1 - (total);
        b[i] += ans2;
        total += ans2;
      }
      if (i % 2 == 1 && total >=0) {
        ans2 += 1 + total;
        b[i] += -ans2;
        total += -ans2;
      }
    }   
    System.out.print(Math.min(ans1,ans2));
  }
}