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.util.Scanner;
public class Main {

	public static void main(String[] args)throws Exception {
		Scanner stdIn=new Scanner(System.in);
		int N=stdIn.nextInt();
		int a[]=new int[N];
		int pla=0,key=0,cun=0;
		int z=0;
		while(z<N) {
			a[z]=stdIn.nextInt();
			key+=a[z];
			if(a[0]<0)
				pla=1;
			if(pla==0) {
				if(z%2==0) {
					if(key<0) {
						cun+=key*-1+1;
						key=1;
					}
					if(key==0) {
						cun+=1;
						key+=1;
					}
				}
				else {
					if(key>0) {
						cun+=key+1;
						key=-1;
					}
					if(key==0) {
						cun+=1;
						key-=1;
					}
				}
			}
			else {
				if(z%2==1) {
					if(key<0) {
						cun+=key*-1+1;
						key+=1;
					}
					if(key==0) {
						cun+=1;
						key+=1;
					}
				}
				else {
					if(key>0) {
						cun+=key+1;
						key=-1;
					}
					if(key==0) {
						cun+=1;
						key-=1;
					}
				}
			}
			z++;
		}
		System.out.println(cun);
	}
}