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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defun read-num (&optional (stream *standard-input*))
  (parse-integer (read-line stream)))

(defun read-list-from-string (str)
  (read-from-string (concatenate 'string "(" str ")")))

(defun read-list (&optional (stream *standard-input*))
  (read-list-from-string (read-line stream)))

(defun satisfy-num (acc val)
  (if (> acc 0)
      (if (< (+ acc val) 0)
	  0
	  (- (+ 1 val acc)))
      (if (> (+ acc val) 0)
	  0
	  (- 1 val acc))))

(defun count-shift (list)
  (let ((acc (car list))
	(sum 0))
    (dolist (e (cdr list) sum)
      (let ((shift (satisfy-num acc e)))
	(incf sum (abs shift))
	(incf acc (+ e shift))))))

(defun solve (list)
  (format t "~D~%" (count-shift list)))
(read-num)
(solve (read-list))