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 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<algorithm>
#include<math.h>
#include<cstring>
#include<queue>
#include<vector>
#include<map>
#include<set>
#include<vector>
using namespace std;
int main() {

	//D
	/*long long int x, y;
	cin >> x >> y;
	if (abs(x - y) <= 1) {
		cout << "Brown" << endl;
	}
	else {

		cout << "Alice" << endl;

	}
	return 0;
	*/


	//C

	int n;
	cin >> n;
	long long int a[100000];
	int i;
	long long int sum = 0, counter = 0, counterB = 0;
	for(i = 0;i<n;i++){
		cin >> a[i];

		if (sum < 0) {
			if (sum + a[i] <= 0) {
				counter = counter + abs(-sum + 1 - a[i]);
				sum  = 1;
			}
			else {
				sum = sum + a[i];
			}
			
		}
		else if (sum > 0){
			if (sum + a[i] >= 0) {
				counter = counter + abs(-sum - 1 - a[i]);
				sum = - 1;
			}
			else {
				sum = sum + a[i];
			}
		}
		else {
			sum = sum + a[i];
		}
		//sum = sum + a[i];
		//cout << counter << ' ';
	}
	//counterB = abs(a[0])+1;
	if (a[0] > 0){
		counterB = a[0] + 1;
		sum = -1;
	}
	else {
		counterB = -a[0] + 1;
		sum = 1;
	}
	for (i = 1; i < n; i++) {
		//cin >> a[i];

		if (sum < 0) {
			if (sum + a[i] <= 0) {
				counterB = counterB + abs(-sum + 1 - a[i]);
				sum = 1;
			}
			else {
				sum = sum + a[i];
			}

		}
		else if (sum > 0) {
			if (sum + a[i] >= 0) {
				counterB = counterB + abs(-sum - 1 - a[i]);
				sum = -1;
			}
			else {
				sum = sum + a[i];
			}
		}
		//sum = sum + a[i];
		//cout << counter << ' ';
	}

	cout << min(counter,counterB) << endl;
	return 0;
	
}