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 <vector>
#include <algorithm>
#include <cmath>
#include <fstream>
#include <bitset>
#include <cstdio>
#include <sstream>
#include <string>
#include <queue>
#include <map>
#include <stack>
#include <set>
#include <cctype>
#include <iomanip>
#include <list>
#include <cstring>

#define INF 2000000000
#define ull unsigned long long int
#define vi vector<int>
#define vii vector<ii>
#define int long long int

#define UNVISITED 0
#define OPENED 1
#define CLOSED 2

#define PI 3.14159265359

#define D(x) cout<<#x<<" : "<<x<<endl
#define P(x) cout << x << endl;

using namespace std;

vector <int> t;

int eval(int t0) {
	
	int prevSum = t0;
	int rep = 0;
	for(int i= 1; i < t.size(); i++) {
		int currSum = prevSum + t[i];
		if(prevSum < 0) {
			if(currSum == 0) {
				currSum = 1; rep++;
			}
			else if(currSum < 0){
				rep += abs(currSum)+1;currSum = 1; 
			}
		}
		else if(prevSum > 0) {
			if(currSum == 0) {
				currSum = -1; rep++;
			}
			else if(currSum > 0){
				rep += abs(currSum)+1; currSum = -1; 
			}
		}
		//cout << currSum << " " << rep << endl;
		prevSum = currSum;
	}	
	return rep;
}

signed main () {
	int n; cin >> n; int a;
	for(int i= 0; i <n; i++) {
		cin >> a; 
		t.push_back(a);
	}
	//cout << eval(t[0]) << endl;
	if(t[0] == 0) cout << min(eval(1)+1, eval(-1)+1) << endl;
	else cout << min(min(eval(t[0]), eval(1)+abs(1-t[0])), eval(-1)+abs(-1-t[0])) << endl;;
	
	
	return 0;
}