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) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] a = new long[n];
		for(int i=0;i<n;i++) a[i] = sc.nextLong();
		sc.close();
		long count1 = 0;
		long sum = 0;
		long lastsum = 0;
		for(int i=0;i<n;i++){
			lastsum = sum;
			sum += a[i];
			if(sum==0){
				if(lastsum>0){
					count1 += 1;
					sum = -1;
				} else if(lastsum<0){
					count1 += 1;
					sum = 1;
				} else {
					if(i<n-1){
						if(a[i+1]>0){
							count1 ++;
							sum = -1;
						} else if (a[i+1]<0){
							count1 ++;
							sum = 1;
						} else {
							count1 += i==0?1:2;
						}
					} else {
						count1 +=2;
					}
				}
			} else if(sum>0&&lastsum>0){
				count1 += sum+1;
				sum = -1;
			} else if(sum<0&&lastsum<0){
				count1 += 1-sum;
				sum = 1;
			}
		}
		sum = 0;
		lastsum = 0;
		long count2 = 0;
		long[] b = new long[n];
		for(int i=0;i<n;i++) b[i] = a[n-i-1];
		for(int i=0;i<n;i++) {
			a[i] = b[i];
		}

		for(int i=0;i<n;i++){
			lastsum = sum;
			sum += a[i];
			if(sum==0){
				if(lastsum>0){
					count2 += 1;
					sum = -1;
				} else if(lastsum<0){
					count2 += 1;
					sum = 1;
				} else {
					if(i<n-1){
						if(a[i+1]>0){
							count2 ++;
							sum = -1;
						} else if (a[i+1]<0){
							count2 ++;
							sum = 1;
						} else {
							count2 += i==0?1:2;
						}
					} else {
						count2 +=2;
					}
				}
			} else if(sum>0&&lastsum>0){
				count2 += sum+1;
				sum = -1;
			} else if(sum<0&&lastsum<0){
				count2 += 1-sum;
				sum = 1;
			}
		}
		System.out.println(Math.min(count1, count2));

	}

}