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 (GCC 5.4.1) (judge verdict: Accepted)

/* Coached by Dukkha */
#include <stdio.h>

#define N 100000

int aa[N];

long long solve(int n, int p) {
	int i, sum;
	long long cnt;

	cnt = sum = 0;
	for (i = 0; i < n; i++) {
		sum += aa[i];
		if (i % 2 == p) {
			if (sum >= 0) {
				cnt += sum + 1;
				sum = -1;
			}
		} else {
			if (sum <= 0) {
				cnt += 1 - sum;
				sum = 1;
			}
		}
	}
	return cnt;
}

int main() {
	int n, i;
	long long ans0, ans1;

	scanf("%d", &n);
	for (i = 0; i < n; i++)
		scanf("%d", &aa[i]);
	ans0 = solve(n, 0);
	ans1 = solve(n, 1);
	printf("%lld\n", ans0 < ans1 ? ans0 : ans1);
	return 0;
}