Problem:
Score : 800 points

Problem Statement

There are N positive integers A_1, A_2, ..., A_N.
Takahashi can perform the following operation on these integers any number of times:

Choose 1 \leq i \leq N and multiply the value of A_i by -2.

Notice that he multiplies it by minus two.

He would like to make A_1 \leq A_2 \leq ... \leq A_N holds.
Find the minimum number of operations required. If it is impossible, print -1.

Constraints

1 \leq N \leq 200000

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the answer.

Sample Input 1

4
3 1 4 1

Sample Output 1

3

One possible solution is:

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now 3, 1, 4, -2.

Choose i=1 and multiply the value of A_1 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, -2.

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, 4.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

0

A_1 \leq A_2 \leq ... \leq A_N holds before any operation is performed.

Sample Input 3

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Sample Output 3

7

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           ;; enclose the form with VALUES to avoid being captured by LOOP macro
           #\# #\> (lambda (s c p) (declare (ignore c p)) `(values ,(read s nil nil t)))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (declare #.OPT)
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setf minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
        (let* ((byte (%read-byte)))
          (if (<= 48 byte 57)
              (setq result (+ (- byte 48)
                              (* 10 (the (integer 0 #.(floor most-positive-fixnum 10))
                                         result))))
              (return (if minus (- result) result))))))))

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;;;
;;; Body
;;;

(defun brute (as)
  #>as
  (let ((n (length as)) res)
    (dotimes (pivot (+ 1 n))
      (let ((as (copy-seq as))
            (sum pivot))
        (loop for j below pivot
              do (setf (aref as j) (* -2 (aref as j))))
        (loop for j from (- pivot 1) downto 0
              unless (= j (- n 1))
              do (loop
                   (when (<= (aref as j) (aref as (+ j 1)))
                     (return))
                   (setf (aref as j) (* -2 (aref as j)))
                   (incf sum)))
        (loop for j from pivot below n
              unless (zerop j)
              do (loop
                   (when (<= (aref as (- j 1)) (aref as j))
                     (return))
                   (setf (aref as j) (* -2 (aref as j)))
                   (incf sum)))
        ;; #>as
        (push sum res)))
    (reverse res)))

(declaim (inline calc-capacity))
(defun calc-capacity (a next-a)
  (assert (<= a next-a))
  (let ((ratio (floor next-a a)))
    (ash (- (integer-length ratio) 1) -1)))

(defun main ()
  (let* ((n (read))
         (as (make-array n :element-type 'uint32)))
    (declare (uint32 n))
    (dotimes (i n)
      (setf (aref as i) (read-fixnum)))
    (labels
        ((build-cumul (as)
           (let (stack ; index . capacity
                 (cumul (make-array (+ n 1) :element-type 'uint32 :initial-element 0)))
             (push (cons (- n 1) #xffffffff) stack) ; sentinel
             (loop for i from (- n 2) downto 0
                   for next-a of-type uint32 = (aref as (+ i 1))
                   for new-value of-type uint32 = (aref cumul (+ i 1))
                   do (loop
                        (when (<= (aref as i) next-a)
                          (let ((cap (calc-capacity (aref as i) next-a)))
                            (when (> cap 0)
                              (push (cons i cap) stack)))
                          (return))
                        (setq next-a (* next-a 4))
                        (let ((node (car stack)))
                          (declare ((cons uint32 uint32) node))
                          (incf new-value (* 2 (- (car node) i)))
                          (decf (cdr node))
                          (when (zerop (cdr node))
                            (pop stack))))
                      (setf (aref cumul i) new-value))
             cumul)))
      (let ((cumul+ (build-cumul as))
            (cumul- (reverse (build-cumul (reverse as)))))
        ;; (dotimes (i (+ n 1))
        ;;   (incf (aref cumul- i) i))
        (println
         (loop for i to n
               minimize (+ (aref cumul+ i)
                           (aref cumul- i)
                           i)))))))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+swank
(defun io-equal (in-string out-string &key (function #'main) (test #'equal))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if
the string output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (eql (uiop:last-char s) #\Linefeed)
                 s
                 (uiop:strcat s uiop:+lf+))))
    (funcall test
             (ensure-last-lf out-string)
             (with-output-to-string (out)
               (let ((*standard-output* out))
                 (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                   (funcall function)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    ;; (run-program "C:/Windows/System32/WindowsPowerShell/v1.0/powershell.exe" '("get-clipboard") :output out)
    (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  "THING := null | string | symbol | pathname

null: run #'MAIN using the text on clipboard as input.
string: run #'MAIN using the string as input.
symbol: alias of FIVEAM:RUN!.
pathname: run #'MAIN using the text file as input."
  (let ((*standard-output* out))
    (etypecase thing
      (null
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "")))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "4
3 1 4 1
"
    "3
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "5
1 2 3 4 5
"
    "0
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097
"
    "7
")))