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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$n = intval(fgets(STDIN));
$array = array_map("intval", explode(" ", trim(fgets(STDIN))));

$min = 10**18;
for($i = 0; $i < 2; $i++){
    $sum = 0;
    $move = 0;
    for($j = 0; $j < $n; $j++){
        $sum+=$array[$j];
        if(($i+$j) % 2 == 0){
            if($sum <= 0){
                $move += 1-$sum;
                $sum += 1-$sum;
            }
        }else{
            if($sum >= 0){
                $move += 1 + $sum;
                $sum -= 1 + $sum;
            }
        }
    }
    $min = min($min, $move);
}
echo $min;