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.*;

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

	public void execute() {
		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();

		long[] A = new long[N];

		for (int i = 0; i < N; i++) {
			long ai = sc.nextLong();
			A[i] = ai;
		}
		long cnt = 0;
		if(A[0] ==0) {
			A[0] = 1;
			long cntA = countOps(A);
			A[0] = -1;
			long cntB = countOps(A);
			cnt = Math.min(cntA, cntB);
		}else {
			cnt = countOps(A);
		}
		System.out.println(cnt);
		sc.close();
	}

	private long countOps(long[] A) {
		long[] arr = A.clone();
		long sum = arr[0];
		long cnt = 0;
		for (int i = 1; i < arr.length; i++) {
			if (sum > 0) {
				if (sum + arr[i] >= 0) {
					cnt += sum + arr[i] + 1;
					arr[i] = -sum - 1;
					sum = -1;
				} else {
					sum = sum + arr[i];
				}
			} else {// sum <0
				if (sum + arr[i] <= 0) {
					cnt += (sum + arr[i]) * -1 + 1;
					arr[i] = -sum + 1;
					sum = 1;
				} else {
					sum = sum + arr[i];
				}
			}
		}
		return cnt;
	}

}