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 <bits/stdc++.h>

using namespace std;
const int N = 1e5 + 5;
int n, a[N];
long long cum[N];
long long go(bool positive) {
	long long sum = 0, cost = 0;
	for (int i = 1; i <= n; ++i) {
		if (positive && cum[i] + sum <= 0) {
			cost += abs(cum[i] + sum) + 1;
			sum += abs(cum[i] + sum) + 1;
		} else if (!positive && cum[i] + sum >= 0) {
			cost += cum[i] + sum + 1;
			sum -= cum[i] + sum + 1;
		}
		positive = !positive;
	}
	return cost;
}
int main() {
#ifndef ONLINE_JUDGE
	freopen("input.in", "r", stdin);
#endif
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		scanf("%d", a + i);
		cum[i] = cum[i - 1] + a[i];
	}
	printf("%lld\n", min(go(true), go(false)));
	
	return 0;
}