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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
import java.text.DecimalFormat;
// warm-up
public class Main {

	static void solve() {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt(), t=n, i=0;
		double[] a = new double[n];
		double o = 0, s = 0;
		while (t-->0) a[i++] = sc.nextDouble();
		for (i=0; i<n; i++) {
			double k=a[i];
			if (s+a[i]==0) a[i]=(-s<0) ? s+1 : 1-s;
			else if ((s<0 && s+a[i]<0)||(s>0 && s+a[i]>0)) a[i]=(s+a[i]<0) ? -s+1 : -s-1;
			o+=Math.abs(k-a[i]);
			s+=a[i];
		}
		System.out.println(new DecimalFormat("#").format(o));
		sc.close();		
	}

	public static void main(String args[]) {
		solve();
	}

}