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

int n, option;
ll ch[2];

int main() {
    cin.sync_with_stdio(0); cin.tie(0);
    cin >> n;
    vector<ll> a(n);
    for (auto& i : a) cin >> i;
    
    for (int i = 0; i < n; ++i) {
        if (a[i] >= 0)
            ch[i % 2] += a[i] + 1;
    }
    
    // Which is going to be negative
    option = (ch[0] >= ch[1]);
    ll cur = 0, ans = 0;
    for (int i = 0; i < n; ++i) {
        cur += a[i];
        if (i % 2 == option && cur >= 0) {
            ans += cur + 1;
            cur = -1;
        } else if (i % 2 != option && cur <= 0) {
            ans += -1ll * (cur - 1);
            cur = 1;
        }
    }
    cout << ans;
}