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) {
		long[] a = null;
		try(Scanner sc = new Scanner(System.in)){
			// N入力 aスペース区切り入力
			a = new long[sc.nextInt()];
			for(int i = 0; i < a.length; i ++) {
				a[i] = sc.nextLong();
			}
		}
		
		long start = a[0];
		boolean isNaturalNum = true;
		if(start < 0) {
			isNaturalNum = false;
		}
		
		long ret = 0L;
		for(int i = 1; i < a.length; i++) {
			
			long temp2 = start + a[i];
			if(isNaturalNum) {
				if(temp2 >= 0) {
					ret += Math.abs(start + a[i]) + 1 ;
					start = -1;
				} else {
					//OK
					start = temp2;
				}
				isNaturalNum = false;
			} else {
				if(temp2 <= 0) {
					ret += Math.abs(start + a[i]) + 1;
					start = 1;
				} else {
					start = temp2;
				}
				isNaturalNum = true;
			}
			
		}
		
		System.out.println(ret);
	}
	
}