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 <stdlib.h>
#include <iostream>
#include <vector>
#include <string>
#include <math.h>
#include <algorithm>
#include <bitset>

using namespace std;

typedef long long int ll;
typedef vector<ll> vl;
typedef vector<string> vs;

#define MAX(a,b) ((a)>(b) ? (a) : (b))
#define MIN(a,b) ((a)<(b) ? (a) : (b))
#define ABS(a) ((a)>0 ? (a) : (a * -1))


int main(){
	ll n, buf, max, ans;
	int flg, flg1;
	ans = 0;
	max = 0;
	buf = 0;
	cin >> n;
	vl a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i]; 
	}

	for (int i = 0; i < n; i++) {
		if (i == 0 && a[i] == 0) {
			if ( a[1] < 0) {
				a[i] = 1;
				ans = 1;
			} else if ( a[1] > 0) {
				a[i] = -1;
				ans = 1;
			}
		}
		buf += a[i];
		if (i == 0) {
			if (a[i] < 0) flg = -1;
			if (a[i] > 0) flg =  1;
		} else {
			if (buf < 0) flg = -1;
			if (buf > 0) flg =  1;
		}


		if (i != 0) {
			if (flg == flg1) {
				if (buf > 0) {
					ans += ABS(buf) + 1;
					buf = -1;
					flg = -1;
				} else if (buf < 0) {
					ans += ABS(buf) + 1;
					buf = 1;
					flg = 1;
				} else if (buf == 0) {
					ans += 1;
					if (flg1 == 1) flg = -1;
					if (flg1 == -1) flg = 1;
				}
				
			}
		}

		flg1 = flg;
	}

	max = ans;
	ans = 0;

	for (int i = 0; i < n; i++) {
		if (i == 0) {
			if ( a[0] > 0 ){
				ans = ABS(buf) + 1;
				buf = -1;
				flg = -1;
			} else if ( a[0] < 0) {
				ans = ABS(buf) + 1;
				buf = 1;
				flg = 1;
			}
		} else {
			buf += a[i];
			if (i == 0) {
				if (a[i] < 0) flg = -1;
				if (a[i] > 0) flg =  1;
			} else {
				if (buf < 0) flg = -1;
				if (buf > 0) flg =  1;
			}
		}


		if (i != 0) {
			if (flg == flg1) {
				if (buf > 0) {
					ans += ABS(buf) + 1;
					buf = -1;
					flg = -1;
				} else if (buf < 0) {
					ans += ABS(buf) + 1;
					buf = 1;
					flg = 1;
				} else if (buf == 0) {
					ans += 1;
					if (flg1 == 1) flg = -1;
					if (flg1 == -1) flg = 1;
				}
				
			}
		}

		flg1 = flg;
	}

	if (ans < max) max = ans; 

	cout << max << endl;
}