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 <bits/stdc++.h>

using namespace std;

typedef long long ll;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n;
	cin >> n;
	vector<ll> a(n);
	for (int i = 0; i < n; i++) cin >> a[i];
	for (int i = 1; i < n; i++) a[i] += a[i - 1];
	ll ans1 = 0, d = 0;
	for (int i = 0; i < n; i++) {
		ll cur = a[i] + d, tmp;
		if (i % 2 == 0) {
			tmp = max(0LL, 1 - cur);
			ans1 += tmp;
			d += tmp;
		} else {
			tmp = max(0LL, cur + 1);
			ans1 += tmp;
			d -= tmp;
		}
	}
	ll ans2 = 0;
	d = 0;
	for (int i = 0; i < n; i++) {
		ll cur = a[i] + d, tmp;
		if (i % 2 == 1) {
			tmp = max(0LL, 1 - cur);
			ans2 += tmp;
			d += tmp;
		} else {
			tmp = max(0LL, cur + 1);
			ans2 += tmp;
			d -= tmp;
		}
	}

	cout << min(ans1, ans2) << endl;
	return 0;
}