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) {
        try (Scanner sc = new Scanner(System.in);) {
            new Main().solve(sc);
        }
    }

    void solve(Scanner sc) {
        int n = sc.nextInt();
        long sumOfP = sc.nextLong();
        long countP = 0;
        long sumOfM = sumOfP;
        long countM = 0;

        if (sumOfP <= 0) {
            countP = -sumOfP + 1;
            sumOfP = 1;
        }

        if (sumOfM >= 0) {
            countM = sumOfM + 1;
            sumOfM = -1;
        }

        for (int i = 1; i < n; i++) {
            long a = sc.nextLong();

            if (sumOfP > 0) {
                if (sumOfP + a >= 0) {
                    countP += sumOfP + a + 1;
                    sumOfP = -1;
                } else {
                    sumOfP += a;
                }
            } else {
                if (sumOfP + a <= 0) {
                    countP += -(sumOfP + a) + 1;
                    sumOfP = 1;
                } else {
                    sumOfP += a;
                }
            }

            if (sumOfM > 0) {
                if (sumOfM + a >= 0) {
                    countM += sumOfM + a + 1;
                    sumOfM = -1;
                } else {
                    sumOfM += a;
                }
            } else {
                if (sumOfM + a <= 0) {
                    countM += -(sumOfM + a) + 1;
                    sumOfM = 1;
                } else {
                    sumOfM += a;
                }
            }
        }

        System.out.println(Math.min(countP, countM));
    }
}