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.util.*;
import java.math.*;
import java.lang.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
		List<Long> list = new ArrayList<>();
		List<Long> sumList = new ArrayList<>();

		long tempSum =0;
		for (int i = 0; i < n; i++) {
			long a = sc.nextLong();
			list.add(a);
			tempSum +=a;
			sumList.add(tempSum);
		}
		// System.out.println("list " + list);

		// start from minus

		long minusSum =0;
		long minusCount =0;
		for (int i = 0; i < n; i++) {
			long a = list.get(i);
			// System.out.println("a  " + a );
			minusSum += a;
			// System.out.println("minusSum " + minusSum);

			if(minusSum>=0 && i%2==0){
				long diff = calcDiff(minusSum);
				minusCount += diff;
				// minusSum -= diff;
				minusSum = -1;
				// System.out.println("diff " + diff);
				// System.out.println("minusSum " + minusSum);
			}
			if(minusSum<=0 && i%2==1){
				long diff = calcDiff(minusSum);
				minusCount += diff;
				// minusSum += diff;
				minusSum = 1;
				// System.out.println("diff " + diff);
				// System.out.println("minusSum " + minusSum);
			}
			// System.out.println();
		}

		// start from plus
		long plusSum =0;
		long plusCount =0;
		for (int i = 0; i < n; i++) {
			long a = list.get(i);
			plusSum += a;
			// System.out.println("plusSum " + plusSum);

			if(plusSum<=0 && i%2==0){
				long diff = calcDiff(plusSum);
				plusCount += diff;
				// plusSum += diff;
				plusSum = 1;
				// System.out.println("diff " + diff);
				// System.out.println("plusSum " + plusSum);
			}
			if(plusSum>=0 && i%2==1){
				long diff = calcDiff(plusSum);
				plusCount += diff;
				// plusSum -= diff;
				plusSum = -1;
				// System.out.println("diff " + diff);
				// System.out.println("plusSum " + plusSum);
			}
			// System.out.println();
		}
		// System.out.println("minusCount " + minusCount);
		// System.out.println("plusCount " + plusCount);


		System.out.println(Math.min(minusCount,plusCount));

	}

	private static long calcDiff(long sum){
		return  Math.abs(sum)+1;
	}
}