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();
        long a[] = new long[n];

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

        long total = 0;
        long man = 0;
        boolean iniZero = true;
        int zeroCount = 0;
        for (int i = 0; i < a.length; i++) {
            if (iniZero) {
                if (a[i] == 0) {
                    zeroCount++;
                } else {
                    iniZero = false;
                    if (Math.abs(a[i]) == 1 && i != 0) {
                        total += a[i] + a[i] > 0 ? 1 : -1;
                        man += 1;
                    } else {
                        total += a[i];
                    }
                }
            } else {
                if (total * (total + a[i]) >= 0) {
                    long x = Math.abs(total + a[i]) + 1;
                    if (total > 0) {
                        total += a[i] - x;
                    } else {
                        total += a[i] + x;
                    }
                    man += x;
                } else {
                    total += a[i];
                }
            }
        }
        if (zeroCount > 0) {
            man += (zeroCount - 1) * 2 + 1;
        }

        System.out.println(man);
    }
}