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: Accepted)

/* "It's okay if you hate me. I hate me too." */

#include <bits/stdc++.h>

using namespace std;

int a[100005];
int n;

long long calc(int MOD) {
	long long sum = 0, res = 0;
	for (int i = 1; i <= n; ++i)  {
		sum += a[i];
		if (i%2 == MOD && sum <= 0) {
			res += (1-sum);
			sum = 1;
		}
		else if (i%2 != MOD && sum >= 0) {
			res += (sum+1);
			sum = -1;
		}
	}
	return res;
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) 
		scanf("%d", &a[i]);
	cout << min(calc(0), calc(1));
	return 0;
}