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: Wrong Answer)

<?php
$N = trim(fgets(STDIN));
$a = explode(" ", trim(fgets(STDIN)));

$plus = (bool)(0 < $a[0]);
$sum = $a[0];
$count = 0;

$plus2 = !$plus;
$sum2 = $plus ? -1 : 1;
$count2 = abs($a[0]) + 1;

function calcCount($plus, $sum, $count){
    global $N, $a;

    for ($i = 1; $i < $N; $i++) {
        if ($plus && (-$sum - 1) < $a[$i]) {
            $count = $count + ($a[$i] - (-$sum - 1));
            $sum = -1;
            $plus = false;
        } elseif (!$plus && (-$sum + 1) > $a[$i]) {
            $count = $count + ((-$sum + 1) - $a[$i]);
            $sum = 1;
            $plus = true;
        } else {
            $sum = $sum + $a[$i];
            $plus = !$plus;
        }
    }

    return $count;
}

echo min(calcCount($plus, $sum, $count),calcCount($plus2, $sum2, $count2));