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: Wrong Answer)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>

int main(void) {
	int n;
	long long int a[100000] = { 0 }, fugo, dif,ans = 0,min = 100000000000000;
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%ld", &a[i]);
	}

	for (fugo = 0; fugo <= 1; fugo++) {
		ans = 0;
		int b[100001] = { 0 };
		for (int i = 0; i < n; i++) {
			dif = 0;
			b[i + 1] = b[i] + a[i];
			if ((i + 1) % 2 == fugo) {
				if (b[i + 1] <= 0) {
					dif += -1 - b[i];
					b[i] += dif;
					dif += 1 - b[i + 1] - dif;
					b[i + 1] += dif;
					ans += dif;
				}
			}
			else {
				if (b[i + 1] >= 0) {
					dif += b[i] - 1;
					b[i] -= dif;
					dif += b[i + 1] + 1 - dif;
					b[i + 1] -= dif;
					ans += dif;
				}
			}
		}

		if (min > ans)min = ans;
	}
	printf("%d\n", min);
}