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;

class Main {
	int n;
	int[] a;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		Main m = new Main(sc);
		m.solve();
		sc.close();
	}

	Main(Scanner sc) {
		n = sc.nextInt();
		a = new int[n];
		for(int i=0;i<n;i++){
			a[i] = sc.nextInt();
		}
	}

	void solve() {
		int sign = (a[0]>=0)?1:-1;
		int cnt = (a[0]==0)?1:0;
		int sum = (a[0]==0)?1:a[0];
		//System.out.println(sum);
		for(int i=1;i<n;i++){
			sum += a[i];
			if(sum*sign>=0){
				cnt += Math.abs(sum) + 1;
				sum = -sign;
			}
			//System.out.println(sum);
			sign *= -1;
		}
		System.out.println(cnt);
	}
}