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 {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int a[] = new int[N];
		for(int i=0; i<N; i++){
			a[i] = sc.nextInt();
		}
		sc.close();
	
		int count = 0;
		int sum = a[0];
		for(int i=1; i<N; i++){
			int diff = checkSum(sum, sum+a[i]);
			count += Math.abs(diff);
			sum = sum+a[i]+diff;
		}
		
		System.out.println(count);

	}
	
	private static int checkSum(int a, int b){
		if ( a>0 && b>=0){
			return -(b+1);
		}else if( a<0 && b<=0){
			return -(b-1);
		}else{
			return 0;
		}
	}

}