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: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] A = new int[N + 1];
        A[0] = 0;
        for (int i= 1; i <= N; ++i) {
            A[i] = sc.nextInt();
        }
        sc.close();

        long sum1 = 0;
        long sum2 = 0;
        long ans1 = 0;
        long ans2 = 0;
        for (int i= 1; i <= N; ++i) {
            sum1 += A[i]; 
            if (i % 2 == 0 && sum1 >= 0) {
                ans1 += Math.abs(sum1) +1;
                sum1 = -1;
            } else if (i % 2 != 0 && sum1 <= 0) {
                ans1 += Math.abs(sum1) + 1;
                sum1 = 1;
            }
        }
        for (int i= 1; i <= N; ++i) {
            sum2 += A[i]; 
            if (i % 2 == 0 && sum2 <= 0) {
                ans2 += Math.abs(sum2) +1;
                sum2 = 1;
            } else if (i % 2 != 0 && sum2 >= 0) {
                ans2 += Math.abs(sum2) + 1;
                sum2 = -1;
            }
        }
        System.out.println(Math.min(ans1, ans2));
    }
}