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;

public class Main {
	@SuppressWarnings("resource")
	public static void main(String args[]) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int a[]=new int[n];
		for(int i=0;i<n;i++) {
			a[i]=scanner.nextInt();
		}
		int r[]=new int[n];
		r[0]=a[0];
		int cnt1=0;
		if(r[0]>=0) {
			cnt1+=Math.abs(-1-r[0]);
			r[0]=-1;
		}
		for(int i=1;i<n;i++) {
			r[i]=r[i-1]+a[i];
			if(i%2==1&&r[i]<=0) {
				cnt1+=Math.abs(1-r[i-1]-a[i]);
				r[i]=1;
			}
			if(i%2==0&&r[i]>=0) {
				cnt1+=Math.abs(-1-r[i-1]-a[i]);
				r[i]=-1;
			}
		}
		r=new int[n];
		r[0]=a[0];
		int cnt2=0;
		if(r[0]<=0) {
			cnt2+=Math.abs(1-r[0]);
			r[0]=1;
		}
		for(int i=1;i<n;i++) {
			r[i]=r[i-1]+a[i];
			if(i%2==1&&r[i]>=0) {
				cnt2+=Math.abs(-1-r[i-1]-a[i]);
				r[i]=-1;
			}
			if(i%2==0&&r[i]<=0) {
				cnt2+=Math.abs(1-r[i-1]-a[i]);
				r[i]=1;
			}
		}
		System.out.println(Math.min(cnt1, cnt2));
	}
}