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: Wrong Answer)

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

int main() {
    int N;
    cin >> N;
    vector<int> a(N);
    for (int i=0; i<N; i++) {
        cin >> a.at(i);
    }
    int ans1 = 0, ans2 = 0, sum = 0;
    for (int i=0; i<N; i++) {
        sum += a.at(i);
        if (i%2 == 0 && sum <= 0) {
            ans1 += 1-sum; //sumは負
            sum = 1;
        }
        else if (i%2 == 1 && sum >= 0) {
            ans1 += sum+1;
            sum = -1;
        }
    }
    sum = 0;
    for (int i=0; i<N; i++) {
        sum += a.at(i);
        if (i%2 == 0 && sum >= 0) {
            ans2 += sum+1;
            sum = -1;
        }
        else if (i%2 == 1 && sum <= 0) {
            ans2 += 1-sum;
            sum = 1;
        }
    }
    int ans = min(ans1, ans2);
    cout << ans << endl;
    return 0;
}