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)

/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		int[] input = new int[n];
		int[] result = new int[n];
		int even = 0;
		int odd = 0;
		boolean sign = true;	//正=true, 負=false
		
		for(int i = 0; i < n; i++) {
			input[i] = sc.nextInt();
			if(i % 2 == 0) {
				even += input[i];
			} else {
				odd += input[i];
			}
		}
		
		if(even > odd) {
			sign = true;
		} else {
			sign = false;
		}
		//System.out.println(Arrays.toString(input));
		//System.out.println(sign + "");
		//System.out.println(counting(input, result, 0, 0, sign));
		counting(input, result, 0, 0, sign);
	}
	
	public static void counting(int[] input, int[] result, int count, int index, boolean sign) {
		
		if(index > 0) {
			result[index] = result[index - 1] + input[index];
		} else {
			result[index] = input[index];
		}
		
		
		if(sign) {
			if(result[index] <= 0) {
				count += Math.abs(result[index]) + 1;
				result[index] = result[index] + Math.abs(result[index]) + 1;
				
			}
			sign = false;
			
		} else {
			if(result[index] >= 0) {
				count += Math.abs(result[index]) + 1;
				result[index] = result[index] - Math.abs(result[index]) - 1;
				
			}
			sign = true;
		}
		
		if(index < result.length - 1) {
			counting(input, result, count, index+1, sign);
		} else {
			System.out.println(count);
		}
	}
}