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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include <string>
#include<vector>
typedef long long ll;

using namespace std;
int main()
{
	int n;
	cin >> n;
	vector<int> as(n);
	for (int i = 0; i < n; i++) {
		cin >> as[i];
	}
	ll kotae1 = 0; //as[0]が正の場合
	int sum1 = 0;
	ll kotae2 = 0; //as[0]が負の場合
	int sum2 = 0;

	
	for (int i = 0; i < n; i++) {
		sum1 += as[i];
		if (i % 2==0){
			if (sum1 <= 0) {
				kotae1 += (1 - sum1);
				sum1 = 1;
			}
		}
		else {
			if (sum1 >= 0) {
				kotae1 += (sum1-(-1));
				sum1 = -1;
			}
		}
	}

	for (int i = 0; i < n; i++) {
		sum2 += as[i];
		if (i % 2 == 1) {
			if (sum2 <= 0) {
				kotae2 += (1 - sum2);
				sum2 = 1;
			}
		}
		else {
			if (sum2 >= 0) {
				kotae2 += (sum2 - (-1));
				sum2 = -1;
			}
		}
	}
	int kotae = 0;
	kotae = kotae1 < kotae2 ? kotae1 : kotae2;

	cout <<kotae<< endl;
	return 0;
}