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();

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

	long[] sum_ = new long[n];

	sum_[0] = a_[0];

	long count1 = 0;
	long count2 = 0;
	//sum_[0] >= 1
	if(sum_[0] < 1){
	    count1 = 1-sum_[0];
	}else{
	}
	for(int i = 1; i < n; i++){
	    sum_[i] = sum_[i-1]+a_[i];
	    if(i % 2 != 0){
		if(sum_[i] <= -1){
		    //OK
		}else{
		    count1 += sum_[i] + 1;
		    sum_[i] = -1;
		}
	    }else{
		if(sum_[i] >= 1){
		    //OK
		}else{
		    count1 += 1 - sum_[i];
		    sum_[i] = 1;
		}
	    }
	}
    
	
	//sum_[0] <= -1
	if(sum_[0] > -1){
	    count2 = sum_[0]+1;
	}else{
	}
	for(int i = 1; i < n; i++){
	    sum_[i] = sum_[i-1]+a_[i];
	    if(i % 2 != 0){
		if(sum_[i] >= 1){
		    //OK
		}else{
		    count2 += 1-sum_[i];
		    sum_[i] = 1;
		}
	    }else{
		if(sum_[i] <= -1){
		    //OK
		}else{
		    count2 += sum_[i]+1;
		    sum_[i] = -1;
		}
	    }
	}
    

	System.out.println(Math.min(count1, count2));
    }
}