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: Accepted)

import java.io.PrintWriter;
import java.util.Scanner;

public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		//入力
		int n = sc.nextInt();
		long[] a = new long[n];
		for(int i = 0; i < n; i++){
			a[i] = sc.nextLong();
		}
		sc.close();

		//処理
		long ans = -1;
		for(int pat = 0; pat < 2; pat++){
			long sum = 0;
			long temp = 0;
			for(int i = 0; i < n; i++){
				sum += a[i];
				if(i % 2 == pat){
					if(sum <= 0){
						temp += Math.abs(sum) + 1;
						sum = 1;
					}
				}else{
					if(sum >= 0){
						temp += Math.abs(sum) + 1;
						sum = -1;
					}
				}
			}

			if(ans == -1){
				ans = temp;
			}else{
				ans = Math.min(ans, temp);
			}
		}

		//出力	
		out.println(ans);
		out.flush();
	}

	static class Pair{
		int w,v;
		public Pair(int a, int b){
			this.w = a;
			this.v = b;
		}
	}
}