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.io.*;
import java.util.*;

public class Main{
    
    public static void main(String args[])throws IOException{
       long c1 = 0;
       long c2 = 0;
       long sum1 = 0;
       long sum2 = 0;
       BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       int n = Integer.parseInt(br.readLine());
       StringTokenizer st = new StringTokenizer(br.readLine());
       for(int i=0;i<n;i++){
           long tmp = Integer.parseInt(st.nextToken());
           sum1 += tmp;
           sum2 += tmp;
           if(i%2==0){
               if(sum1<=0){
                   c1 += Math.abs(sum1)+1;
                   sum1 = 1;
               }
               if(sum2>=0){
                   c2 += Math.abs(sum2)+1;
                   sum2 = -1;
               }
           }else{
               if(sum1>=0){
                   c1 += Math.abs(sum1)+1;
                   sum1 = -1;
               }
               if(sum2<=0){
                   c2 += Math.abs(sum2)+1;
                   sum2 = 1;
               }
           }
       }
        System.out.println(Math.min(c1, c2));
    }
     
}