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.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        long[] a1 = new long[n];
        long[] a2 = new long[n];
        for (int i = 0; i < n; i++) {
            long temp = Long.parseLong(sc.next());
            a1[i] = temp;
            a2[i] = temp;
        }
        long ans1 = 0;
        long ans2 = 0;
        long temp = 0;
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0 && temp + a1[i] >= 0) {
                ans1 += temp + a1[i] + 1;
                a1[i] -= temp + a1[i] + 1;
            }
            if (i % 2 != 0 && temp + a1[i] <= 0) {
                ans1 += Math.abs(temp + a1[i] - 1);
                a1[i] += Math.abs(temp + a1[i] - 1);
            }
            temp += a1[i];
        }
        if (Arrays.stream(a1).sum() == 0) {
            ans1++;
        }
        temp = 0;
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0 && temp + a2[i] <= 0) {
                ans2 += Math.abs(temp + a2[i] - 1);
                a2[i] += Math.abs(temp + a2[i] - 1);
            }
            if (i % 2 != 0 && temp + a2[i] >= 0) {
                ans2 += temp + a2[i] + 1;
                a2[i] -= temp + a2[i] + 1;
            }
            temp += a2[i];
        }
        if (Arrays.stream(a2).sum() == 0) {
            ans2++;
        }
        System.out.println(Math.min(ans1, ans2));
    }
}