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 {

	static String[] alphabet = { "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q",
			"r", "s", "t", "u", "v", "w", "x", "y", "z" };

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long[] ary = new long[N];
		for (int i = 0; i < N; i++) {
			ary[i] = sc.nextLong();
		}
		long cstKisu = 0;
		long[] aryKisu = new long[N];
		System.arraycopy(ary, 0, aryKisu, 0, ary.length);
		long sumKisu = 0;
		for (int i = 0; i < aryKisu.length; i++) {
			sumKisu += aryKisu[i];
			if (i % 2 == 0) {
				if (sumKisu <= 0) {
					aryKisu[i] += 1 - sumKisu;
					cstKisu += 1 - sumKisu;
					sumKisu = 1;
				}
			} else {
				if (sumKisu >= 0) {
					aryKisu[i] -= sumKisu + 1;
					cstKisu += sumKisu + 1;
					sumKisu = -1;
				}
			}
		}

		long cstGusu = 0;
		long[] aryGusu = new long[N];
		System.arraycopy(ary, 0, aryGusu, 0, ary.length);
		long sumGusu = 0;
		for (int i = 0; i < aryGusu.length; i++) {
			sumGusu += aryGusu[i];
			if (i % 2 == 0) {
				if (sumGusu >= 0) {
					aryGusu[i] -= sumGusu + 1;
					cstGusu += sumGusu + 1;
					sumGusu = -1;
				}
			} else {
				if (sumGusu <= 0) {
					aryGusu[i] += 1 - sumGusu;
					cstGusu += 1 - sumGusu;
					sumGusu = 1;
				}
			}
		}
		System.out.println(Math.min(cstGusu, cstKisu));

	}

}