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.*;

public class Main {
	
	public static void main (String[] args){
		Scanner cin = new Scanner(System.in);
		int N = cin.nextInt();
		int[] array = new int[N];
		for(int i=0;i<N;i++){
			array[i] = cin.nextInt();
		}
		int res = 0;
		if (array[0] == 0) {
			if (array[1] >= 0) {
				array[0] = -1;
			} else {
				array[0] = 1;
			}
			res++;
		}
		int sum = array[0];
		for (int i=0;i<N;i++){
			int temp = sum + array[i];
			if (temp * sum == 0){
				if (sum > 0) {
					//temp
					array[i]--;
				} else {
					array[i]++;
				}
				res++;
			} else if (temp * sum > 0) {
				if (sum > 0) {
					 //要令temp = -1才行
					res+=Math.abs(-1 - sum - array[i]);
					sum = -1;
				} else {
					res+= Math.abs(1-sum -array[i]);
					sum = 1;
				}
			} else {
				sum = temp;
			}
		}
		System.out.println(res);
	}
}