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: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main{
    static int n;
    static long[] a;
    static long count;
    static  long sum;
    public static void main(String[] args) throws IOException{
        MyReader r = new MyReader();
        n = r.i();
        a = r.ll();
        sum = a[0];
        count = 0;
        if(a[0] == 0){
            count = 1;
            sum = 1;
            solve();
            long temp = count;
            count = 1;
            sum = -1;
            solve();
            count = Math.min(count, temp);
        } else {
            solve();
            long temp = count;
            sum = -a[1]-1;
            count = Math.abs(a[0]+a[1]+1);
            solve();
            temp = Math.min(temp, count);
            sum = -a[1]+1;
            count = Math.abs(a[0]+a[1]-1);
            solve();
            count = Math.min(temp, count);
        }
        println(count);
    }

    static void solve(){
        for(int i = 1; i < n; i++){
            if(sum < 0){
                if(a[i]+sum <= 0){
                    count += -(a[i]+sum)+1;
                    sum = 1;
                } else
                    sum = a[i]+sum;
            } else{
                if(a[i]+sum>=0){
                    count += a[i]+sum+1;
                    sum = -1;
                } else
                    sum = a[i]+sum;
            }            
        }
    }

    static void print(Object o){
        System.out.print(o.toString());
    }

    static void println(Object o){
        System.out.println(o.toString());
    }

    static int Int(String s){
        return Integer.parseInt(s);
    }

    static long Long(String s){
        return Long.parseLong(s);
    }
    static class MyReader extends BufferedReader{
        MyReader(){
            super(new InputStreamReader(System.in));
        }

        String s() throws IOException{
            return readLine();
        }

        String[] ss() throws IOException{
            return s().split(" ");
        }

        int i() throws IOException{
            return Int(s());
        }

        int[] ii() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            int[] ii = new int[size];
            for(int j = 0; j < size; j++) ii[j] = Integer.parseInt(ss[j]);
            return ii;
        }

        long l() throws IOException{
            return Long(s());
        }

        long[] ll() throws IOException{
            String[] ss = ss();
            int size = ss.length;
            long[] ll = new long[size];
            for(int j = 0; j < size; j++) ll[j] = Long.parseLong(ss[j]);            
            return ll;
        }
    }
}