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: Accepted)

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <stdio.h>
#include <cstring>
#include <queue>
#include <stack>
#include <functional>
#include <math.h>
#include <iomanip>
using namespace std;
#define Would
#define you
const int INF = 999999999;
const int MOD = 1e9 + 7;
const double pi = 3.141592653589793238;

long long n, k[100005], ans, cou, cou2;
int main() {
	cin >> n;
	for (int i = 0; i < n; ++i) { cin >> k[i]; }
	//[0]=minus
	for (int i = 0; i < n; ++i) {
		ans += k[i];
		if (i % 2 == 0 && ans <= 0) {
			cou += 1 - ans;
			ans = 1;
		}
		if (i % 2 == 1 && ans >= 0) {
			cou += ans + 1;
			ans = -1;
		}
	}
	ans = 0;
	//[0]=plus
	for (int i = 0; i < n; ++i) {
		ans += k[i];
		if (i % 2 == 1 && ans <= 0) {
			cou2 += 1 - ans;
			ans = 1;
		}
		if (i % 2 == 0 && ans >= 0) {
			cou2 += ans + 1;
			ans = -1;
		}
	}
	cout << min(cou, cou2) << endl;
}