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;

class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int N=sc.nextInt();
		long[] k=new long[N];
		for(int i=0; i<N; i++) {
			k[i]=sc.nextLong();
		}

		for(int i=1; i<N; i++) {
			k[i]=k[i-1]+k[i];
		}
		long counter=0;
		if(k[0]>0) {
			counter=1;
		}
		else {
			counter=-1;
		}

		long[] tasu=new long[N];
		long kaz=0;
		for(int i=0; i<N; i++) {
			tasu[i]=0;
		}

		for(int i=0; i<N; i++) {
			long tmp=counter*(k[i]+tasu[i]);
			if(tmp>0) {
				//条件を満たすのでOK
			}
			else if(tmp<0){
				if((k[i]+tasu[i])>0) {
					long tt=(k[i]+tasu[i])+1;
					kaz+=tt;
					tasu[i]-=tt;
				}
				else if((k[i]+tasu[i])<0) {
					long tt=((k[i]+tasu[i])-1)*-1;
					kaz+=tt;
					tasu[i]+=tt;
				}
			}
			if(tmp==0) {
				if(counter==-1) {
					tasu[i]--;
				}
				else if(counter==1) {
					tasu[i]++;
				}
				kaz++;
			}
			if(i!=N-1) {
				tasu[i+1]=tasu[i];
			}
			counter*=-1;
		}
		System.out.println(kaz);
	}
}