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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		long sumi = 0;
		long sumi1 = 0;
		long countPlus = 0;
		long countMinus = 0;
		long[] a = new long[n];
		for(int i = 0; i < n; i++) {
			a[i] = Long.valueOf(scan.next());
		}
		
		// 奇数がプラス
		for(int i = 0; i < n; i++) {
			sumi1 = sumi + a[i];
			if((i + 1) % 2 == 1) {
				if(sumi1 <= 0) {
					countPlus += Math.abs(sumi1) + 1;
					sumi1 += Math.abs(sumi1) + 1;
				}
			} else if((i + 1) % 2 == 0) {
				if(sumi1 >= 0) {
					countPlus += Math.abs(sumi1) + 1;
					sumi1 -= Math.abs(sumi1) + 1;
				}
			}
			sumi = sumi1;
		}
		sumi = 0;
		sumi1 = 0;
		
		// 奇数がマイナス
		for(int i = 0; i < n; i++) {
			sumi1 = sumi + a[i];
			if((i + 1) % 2 == 1) {
				if(sumi1 >= 0) {
					countMinus += Math.abs(sumi1) + 1;
					sumi1 -= Math.abs(sumi1) + 1;
				}
			} else if((i + 1) % 2 == 0) {
				if(sumi1 <= 0) {
					countMinus += Math.abs(sumi1) + 1;
					sumi1 += Math.abs(sumi1) + 1;
				}
			}
			sumi = sumi1;
		}
		
		if(countPlus < countMinus) {
			System.out.println(countPlus);
		} else {
			System.out.println(countMinus);
		}
		
		scan.close();

	}

}