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.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.concurrent.SynchronousQueue;

class Main {
	public static void main(String[] args) throws IOException {
		new Main().run();
	}

	void run() {
		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();
		}
		long[] sum = new long[n];
		for (int i = 0; i < n; ++i) {
			sum[i] = (i > 0 ? sum[i - 1] : 0) + a[i];
		}

		long ans = Long.MAX_VALUE / 16;
		out: for (int add = -1; add <= 1; ++add) {
			long cnt = 0;
			long d = add;
			cnt = Math.abs(d);
			if(a[0]+d==0)continue;
			for (int i = 1; i < n; ++i) {
				if (sign(sum[i] + d) * sign(sum[i - 1] + d) < 0) {
					continue;
				}
				if (sum[i - 1] + d > 0 && sum[i] + d >= 0) {
					cnt += sum[i] + d + 1;
					d -= sum[i] + d + 1;
				} else if (sum[i - 1] + d < 0 && sum[i] + d <= 0) {
					cnt += -(sum[i] + d) + 1;
					d += -(sum[i] + d) + 1;
				} else {
					continue out;
				}
			}
			ans = Math.min(ans, cnt);
		}
		System.out.println(ans);

	}

	int sign(long x) {
		return Long.compare(x, 0);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}