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
    fscanf(STDIN, "%d\n", $n);
    $a = explode(" ", trim(fgets(STDIN)));

    $score_a = 0;
    $score_b = 0;

    $tmp = 0;

    for ($i = 0; $i < $n; $i++) {
        $tmp += $a[$i];
        if ($i % 2 == 0) {
            if ($tmp >= 0) {
                $score_a += $tmp + 1;
                $tmp -= ($tmp + 1);
            }
        } else {
            if ($tmp <= 0) {
                $score_a += -($tmp - 1);
                $tmp += -($tmp - 1);
            }
        }
    }

    $tmp = 0;

    for ($i = 0; $i < $n; $i++) {
        $tmp += $a[$i];
        if ($i % 2 != 0) {
            if ($tmp >= 0) {
                $score_b += $tmp + 1;
                $tmp -= ($tmp + 1);
            }
        } else {
            if ($tmp <= 0) {
                $score_b += -($tmp - 1);
                $tmp += -($tmp - 1);
            }
        }
    }

    echo min($score_a, $score_b) . PHP_EOL;