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 scan = new Scanner(System.in);

	int n = scan.nextInt();

	int[] a_ = new int[n];
	for(int i = 0; i < n; i++){
	    a_[i] = scan.nextInt();
	}

	int count = 0;
	int[] sum_ = new int[n];
	//i % 2 == 1 : sum_[i] <= -1
	if(a_[0] > 0){
	    sum_[0] = a_[0];
	    for(int i = 1; i < n;){
		sum_[i] = sum_[i-1] + a_[i];
		if(i % 2 != 0){
		    if(sum_[i] < 0){
			//OK
			i++;
		    }else{
			if(sum_[i-1] > 1){
			    sum_[i-1]--;			   
			}else{
			    a_[i]--;
			}
			count++;
		    }
		}else{
		    if(sum_[i] > 0){
			//OK
			i++;
		    }else{
			if(sum_[i-1] < -1){
			    sum_[i-1]++;			    
			}else{
			    a_[i]++;
			}
			count++;
		    }
		}if(count == 10)break;
	    }
	}else{
	    sum_[0] = a_[0];
	    for(int i = 1; i < n;){
		sum_[i] = sum_[i-1] + a_[i];
		if(i % 2 != 0){
		    if(sum_[i] > 0){
			//OK
			i++;
		    }else{
			if(sum_[i-1] < -1){
			    sum_[i-1]++;
			}else{
			    a_[i]++;
			}
			count++;
		    }
		}else{
		    if(sum_[i] < 0){
			//OK
			i++;
		    }else{
			if(sum_[i-1] > 1){
			    sum_[i-1]--;
			}else{
			    a_[i]--;
			}
			count++;
		    }
		}
	    }
	}

	System.out.println(count);
    }
}