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.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Long> a = new ArrayList<>();
        IntStream.range(0, n).forEach(i -> a.add(sc.nextLong()));


        Long plusMinusStep = 0L;
        Long minusPlusStep = 0L;
        Long plusMinusSum = 0L;
        Long minusPlusSum = 0L;
        for (int i = 0; i < n; i++) {
            Long target = a.get(i);
            if (i % 2 == 1) {
                if (plusMinusSum + target >= 0) {
                    plusMinusStep += Math.abs(plusMinusSum + target) + 1;
                    plusMinusSum = -1L;
                } else {
                    plusMinusSum += target;
                }
                if (minusPlusSum + target <= 0) {
                    minusPlusStep += Math.abs(minusPlusSum + target) + 1;
                    minusPlusSum = 1L;
                } else {
                    minusPlusSum += target;
                }
                continue;
            }
            if (plusMinusSum + target <= 0) {
                plusMinusStep += Math.abs(plusMinusSum + target) + 1;
                plusMinusSum = 1L;
            } else {
                plusMinusSum += target;
            }
            if (minusPlusSum + target >= 0) {
                minusPlusStep += Math.abs(minusPlusSum + target) + 1;
                minusPlusSum = -1L;
            } else {
                minusPlusSum += target;
            }
        }
        System.out.println(Math.min(plusMinusStep, minusPlusStep));
    }

}