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)

#include<iostream>
#include<algorithm>
using LL = long long;
LL n;
LL a[100000];
LL sum[100001];
LL costg, costk;
int main() {
	std::cin >> n;
	for (int i = 0; i < n; i++) {
		std::cin >> a[i];
	}
	for (int i = 0; i < n; i++) {
		sum[i + 1] += sum[i] + a[i];
		if (i % 2 == 0) {
			if (sum[i + 1] <= 0) {
				costg += std::abs(1 - sum[i + 1]);
				sum[i + 1] = 1;
			}
		}
		else {
			if (sum[i + 1] >= 0) {
				costg += std::abs(-1 - sum[i + 1]);
				sum[i + 1] = -1;
			}
		}
	}
	for (int j = 1; j <= n; j++) {
		sum[j] = 0;
	}
	for (int i = 0; i < n; i++) {
		sum[i + 1] += sum[i] + a[i];
		if (i % 2 != 0) {
			if (sum[i + 1] <= 0) {
				costk += std::abs(1 - sum[i + 1]);
				sum[i + 1] = 1;
			}
		}
		else {
			if (sum[i + 1] >= 0) {
				costk += std::abs(-1 - sum[i + 1]);
				sum[i + 1] = -1;
			}
		}
	}
	std::cout << std::min(costg, costk) << std::endl;
	return 0;
}