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: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}
	public void run() {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int a[]=new int[n];
		a[0]=sc.nextInt();
		int cnt=0;
		for(int i=1; i<n; i++) {
			int v=sc.nextInt();
			if(a[i-1]>0) {
				if(a[i-1]+v>=0) {
					while(a[i-1]+v>=0) {
						v--;
						cnt++;
					}
				}
			} else {
				if(a[i-1]+v<=0) {
					while(a[i-1]+v<=0) {
						v++;
						cnt++;
					}
				}
			}
			a[i]=a[i-1]+v;
		}
		System.out.println(cnt);
		sc.close();
	}

}