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<stdio.h>
#include<stdbool.h>
#include<string>
#include<iostream>
#include<math.h>
#include<vector>
#include<set>
#include<algorithm>
#include<utility>
#include<list>
typedef long long ll;
using namespace std;
ll a[100010] = { 0 };

ll sequence(ll n) {
	ll sum = 0, count = 0;
	bool sign = true;//true is defined by plus
	if (a[1] > 0) {
		sum = a[1];
		sign = false;
		for (ll i = 2;i <= n;i++) {
			sum += a[i];
			if (!sign) {
				if (sum > 0) {
					count += sum + 1;
					sum = sum - sum - 1;
					sign = true;
				}
				else {
					if (sum == 0) {
						count++;
						sum -= 1;
						sign = true;
					}
					else sign = true;
				}
			}
			else {
				if (sum < 0) {
					count += -sum + 1;
					sum = sum - sum + 1;
					sign = false;
				}
				else {
					if (sum == 0) {
						count++;
						sum += 1;
						sign = false;
					}
					else sign = false;
				}
			}
		}	
	}
	else {
		if (a[1] < 0) {
			sum = a[1];
			sign = true;
			for (ll i = 2;i <= n;i++) {
				sum += a[i];
				if (!sign) {
					if (sum > 0) {
						count += sum + 1;
						sum = sum - sum - 1;
						sign = true;
					}
					else {
						if (sum == 0) {
							count++;
							sum -= 1;
							sign = true;
						}
						else sign = true;
					}
				}
				else {
					if (sum < 0) {
						count += -sum + 1;
						sum = sum - sum + 1;
						sign = false;
					}
					else {
						if (sum == 0) {
							count++;
							sum += 1;
							sign = false;
						}
						else sign = false;
					}
				}
			}
		}
		else {
			count++;
			sum = 1;
			sign = false;
				for (ll i = 2;i <= n;i++) {
					sum += a[i];
					if (!sign) {
						if (sum > 0) {
							count += sum + 1;
							sum = sum - sum - 1;
							sign = true;
						}
						else {
							if (sum == 0) {
								count++;
								sum -= 1;
								sign = true;
							}
							else sign = true;
						}
					}
					else {
						if (sum < 0) {
							count += -sum + 1;
							sum = sum - sum + 1;
							sign = false;
						}
						else {
							if (sum == 0) {
								count++;
								sum += 1;
								sign = false;;
							}
							else sign = false;
						}
					}
				}
		}
	}
	return count;
}

int main() {
	ll n, sum = 0, count = 0;
	cin >> n;
	for (ll i = 1;i <= n;i++)cin >> a[i];
	cout << sequence(n) << endl;
	return 0;
}