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.ArrayList;
import java.util.Scanner;


public class Main {
	 public static void main(String args[]){
			Scanner sc = new Scanner(System.in);
			// 整数の入力
			int n = sc.nextInt();
			int a[] = new int[n];
			for(int i = 0;i<a.length;i++)
			{
				a[i] = sc.nextInt();
			}
			int b[] = new int[n];
			b[0] = a[0];
			int count = 0;
			for(int i = 0;i<a.length-1;i++)
			{
				b[i+1] = b[i] + a[i+1]; 
				if(b[i+1]*b[i]>0)
				{
					count += Math.abs(b[i+1])+1;
					if(b[i+1]>0) b[i+1]=-1;
					else b[i+1] = 1;
				}
				else if(b[i+1] == 0)
				{
					if(b[i]>0) b[i+1]=-1;
					else b[i+1] = 1;
					count++;
				}
			}
			System.out.println(count);
			
		  }

}