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.Scanner;

public class Main {

    static long ANS_POSI;
    static long ANS_NEGA;
    static int N;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        N = Integer.parseInt(sc.nextLine());

        long[] a = new long[N];
        for (int i = 0; i < N; i++) {
            long elm = Long.parseLong(sc.next());
            a[i] = elm;
        }

        solve(a);

        System.out.println(Math.min(ANS_POSI, ANS_NEGA));
    }


    private static void solve(long[] a) {
        long posi = 0;
        long nega = 0;
        for (int i = 0; i < N; i++) {
            // 前回のループで変更があった場合は、1か-1になっている値に配列値を合算して合計値としている。
            posi += a[i];
            nega += a[i];
            if (i % 2 == 0) {
                if (posi >= 0) {
                    ANS_POSI += posi + 1;
                    posi = -1;
                }
                if (nega <= 0) {
                    ANS_NEGA -= nega - 1;
                    nega = 1;
                }
            } else {
                if (posi <= 0) {
                    ANS_POSI -= posi - 1;
                    posi = 1;
                }
                if (nega >= 0) {
                    ANS_NEGA += nega + 1;
                    nega = -1;
                }
            }
        }
    }
}