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 {

	void run() {
		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();
			int[] a = new int[n];
			for(int i=0;i<n;i++) {
				a[i] = sc.nextInt();
			}
			
			int sum1 = 0;
			int cnt1 = 0;
			// a[0] > 0
			for(int i=0;i<n;i++) {
				sum1 += a[i];
				if(i%2==0 && sum1 <= 0) {
					cnt1 += (1-sum1);
					sum1 = 1;
				}else if(i%2==1 && sum1 >= 0) {
					cnt1 += (1+sum1);
					sum1 = -1;
				}
			}
			
			int sum2 = 0;
			int cnt2 = 0;
			// a[0] < 0
			for(int i=0;i<n;i++) {
				sum2 += a[i];
				if(i%2==1 && sum2 <= 0) {
					cnt2 += (1-sum2);
					sum2 = 1;
				}else if(i%2==0 && sum2 >= 0) {
					cnt2 += (1+sum2);
					sum2 = -1;
				}
			}
			
			System.out.println(Math.min(cnt1, cnt2));
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}
	
}