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 in = new Scanner(System.in);

		int n = in.nextInt();
		int[] a = new int[n];

		boolean flag = true;
		int sum = 0, ans = 0;
		int i = 1;

		for (int j = 0; j < a.length; j++) {
			a[j] = in.nextInt();
		}

		if (a[0] != 0) {
			sum += a[0];
			flag = a[0] > 0;
		} else {
			++ans;
			for (; i < a.length; i++) {
				if (a[i] != 0) {
					flag = a[i] > 0;
					if (flag) {
						sum = a[i] - 1;

					} else {
						sum = a[i] + 1;
					}
					break;
				}
				ans += 2;
			}
		}

		for (; i < a.length; i++) {
			if (flag && sum + a[i] >= 0) {
				ans += sum + a[i] + 1;
				sum = -1;
				flag = false;
			} else if (!flag && sum + a[i] <= 0) {
				ans += 1 - (sum + a[i]);
				sum = 1;
				flag = true;
			} else {
				sum += a[i];
				flag = sum > 0;
			}
		}
		System.out.println(ans);
	}

}