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)

#include <stdio.h>

int main()
{
	int i, n, a[100001];
	scanf("%d", &n);
	for (i = 1; i <= n; i++) scanf("%d", &(a[i]));
	
	int j, parity;
	long long ans[2], sum[2];
	if (a[1] > 0) {
		sum[0] = a[1];
		sum[1] = -1;
		ans[0] = 0;
		ans[1] = a[1] + 1;
	} else if (a[1] < 0) {
		sum[0] = 1;
		sum[1] = a[1];
		ans[0] = 1 - a[1];
		ans[1] = 0;
	} else {
		sum[0] = 1;
		sum[1] = -1;
		ans[0] = 1;
		ans[1] = 1;
	}
	for (i = 2; i <= n; i++) {
		for (j = 0; j < 2; j++) {
			parity = (i + j) % 2 * 2 - 1;
			if ((sum[j] + a[i]) * parity <= 0) {
				ans[j] += 1 - (sum[j] + a[i]) * parity;
				sum[j] = parity;
			} else sum[j] += a[i];
		}
	}
	
	printf("%lld\n", (ans[0] < ans[1])? ans[0]: ans[1]);
	fflush(stdout);
	return 0;
}