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.*;

public class Main{
    public static void main(String[] args){
            
        Scanner sc = new Scanner(System.in);		                                        
           
        int n = sc.nextInt();
        
        long[] a = new long[n];
        
        for(int i = 0;i < n;i++){
            a[i] = sc.nextLong();
        }
                   
        long sum = 0;
        long cost = 0;
        long ans = Long.MAX_VALUE;
        // +-+-
        for (int i = 0; i < n; i++) {
            sum += a[i];
            if (i % 2 == 0) {
                if (sum <= 0) {
                    cost += -sum + 1;
                    sum = 1;
                }
            } else {
                if (sum >= 0) {
                    cost += sum + 1;
                    sum = -1;
                }
            }
        }
        ans = Math.min(ans, cost);
        sum = 0;
        cost = 0;
        // -+-+
        for (int i = 0; i < n; i++) {
            sum += a[i];
            if (i % 2 == 0) {
                if (sum >= 0) {
                    cost += sum + 1;
                    sum = -1;
                }
            } else {
                if (sum <= 0) {
                    cost += -sum + 1;
                    sum = 1;
                }
            }
        }
        ans = Math.min(ans, cost);
        System.out.println(ans);           
                      
    }    
    
}