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;
typedef long long ll;
map<ll, map<ll, int> >mp, vis;
int solve(ll x, ll y){
  if(x <= 1 && y <= 1)return 0;
  if(vis[x][y])return mp[x][y];
  vis[x][y] = true;
  int &ret = mp[x][y];
  ret = 1;
  swap(x, y);
  if(y >= 2){
    ll cur = y/2;
    int cnt = 30;
    while(cur && cnt){
      ret &= solve(x + cur, y - (cur * 2));
      cur--;
      cnt--;
    }
  }
  swap(x, y);
  if(y >= 2){
    ll cur = y/2;
    int cnt = 30;
    while(cur && cnt){
      ret &= solve(x + cur, y - (cur * 2));
      cur--;
      cnt--;
    }
  }
  ret = !ret;
  return ret;
}
int main(){
  ll x,y ;
  cin >> x >> y;
  cout << (solve(x, y)?  "Alice" : "Brown");
}