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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        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 num1 = 0;
        int tmp1 = 0;
        //+-+-
        for(int i=0; i<n; i++) {
            tmp1 += a[i];
            if(i % 2 == 0) {
                if(tmp1 <= 0) {
                    num1 += Math.abs(tmp1) + 1;
                    tmp1 += Math.abs(tmp1) + 1;
                }
            } else {
                if(tmp1 >= 0) {
                    num1 += Math.abs(tmp1) + 1;
                    tmp1 -= Math.abs(tmp1) + 1;
                }
            }
        }

        int num2 = 0;
        int tmp2 = 0;
        //-+-+
        for(int i=0; i<n; i++) {
            tmp2 += a[i];
            if(i % 2 != 0) {
                if(tmp2 <= 0) {
                    num2 += Math.abs(tmp2) + 1;
                    tmp2 += Math.abs(tmp2) + 1;
                }
            } else {
                if(tmp2 >= 0) {
                    num2 += Math.abs(tmp2) + 1;
                    tmp2 -= Math.abs(tmp2) + 1;
                }
            }
        }
        System.out.println(Math.min(num1,num2));
    }
}