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<bits/stdc++.h>
using namespace std;

long long n;
long long arr[100005];

int main(){
	cin >> n;
	for(long long i = 0; i < n; i++){
		cin >> arr[i];
	}

	long long ans = LONG_MAX;

	long long tmp = 0;
	long long cur = 0;
	//positive start
	for(long long i = 0; i < n; i++){
		if(i%2 == 0){//have to be positive
			if(cur + arr[i] <= 0){
				long long addi = 1 - cur - arr[i];
				tmp += abs(addi);
				cur = 1;
			}else{
				cur = cur + arr[i];
			}
		}else{
			if(cur + arr[i] >= 0){
				long long addi = -1 - cur - arr[i];
				tmp += abs(addi);
				cur = -1;
			}else{
				cur = cur + arr[i];
			}
		}
	}
	ans = min(ans, tmp);

	tmp = 0;
	cur = 0;
	//negative start
	for(long long i = 0; i < n; i++){
		if(i%2 == 0){//negative
			if(cur + arr[i] >= 0){
				long long addi = -1 - cur - arr[i];
				tmp += abs(addi);
				cur = -1;
			}else{
				cur = cur + arr[i];
			}
		}else{
			if(cur + arr[i] <= 0){
				long long addi = 1 - cur - arr[i];
				tmp += abs(addi);
				cur = 1;
			}else{
				cur = cur + arr[i];
			}
		}
	}
	ans = min(ans, tmp);

	cout << ans << endl;
}