;; -*- 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
;;;
;;; Quicksort
;;;

;; Note: Not randomized; the worst case time complexity is O(n^2).

(declaim (inline %median3))
(defun %median3 (x y z order)
  (if (funcall order x y)
      (if (funcall order y z)
          y
          (if (funcall order z x)
              x
              z))
      (if (funcall order z y)
          y
          (if (funcall order x z)
              x
              z))))

(declaim (inline quicksort-by2!))
(defun quicksort-by2! (vector order)
  "Destructively sorts VECTOR by two elements. This function regards
each (VECTOR[i], VECTOR[i+1]) for even i as an element, and compares only the
first elements (i.e. VECTOR[i] for even i)."
  (declare (vector vector))
  (labels
      ((recur (left right)
         (when (< left right)
           (let* ((l left)
                  (r right)
                  (pivot (%median3 (aref vector l)
                                   (aref vector (ash (ash (+ l r) -2) 1))
                                   (aref vector r)
                                   order)))
             (declare ((integer 0 #.most-positive-fixnum) l r))
             (loop (loop while (funcall order (aref vector l) pivot)
                         do (incf l 2))
                   (loop while (funcall order pivot (aref vector r))
                         do (decf r 2))
                   (when (>= l r)
                     (return))
                   (rotatef (aref vector l) (aref vector r))
                   (rotatef (aref vector (+ l 1)) (aref vector (+ r 1)))
                   (incf l 2)
                   (decf r 2))
             (recur left (- l 2))
             (recur (+ r 2) right)))))
    (recur 0 (- (length vector) 2))
    vector))

;;;
;;; Disjoint set by Union-Find algorithm
;;;

(defstruct (disjoint-set
            (:constructor make-disjoint-set
                (size &aux (data (make-array size :element-type 'fixnum :initial-element -1))))
            (:conc-name ds-))
  (data nil :type (simple-array fixnum (*))))

(declaim (ftype (function * (values (mod #.array-total-size-limit) &optional)) ds-root))
(defun ds-root (disjoint-set x)
  "Returns the root of X."
  (declare #.OPT
           ((mod #.array-total-size-limit) x))
  (let ((data (ds-data disjoint-set)))
    (if (< (aref data x) 0)
        x
        (setf (aref data x)
              (ds-root disjoint-set (aref data x))))))

(declaim (inline ds-unite!))
(defun ds-unite! (disjoint-set x1 x2)
  "Destructively unites X1 and X2 and returns true iff X1 and X2 become
connected for the first time."
  (let ((root1 (ds-root disjoint-set x1))
        (root2 (ds-root disjoint-set x2)))
    (unless (= root1 root2)
      (let ((data (ds-data disjoint-set)))
        ;; ensure the size of root1 >= the size of root2
        (when (> (aref data root1) (aref data root2))
          (rotatef root1 root2))
        (incf (aref data root1) (aref data root2))
        (setf (aref data root2) root1)))))

(declaim (inline ds-connected-p))
(defun ds-connected-p (disjoint-set x1 x2)
  "Returns true iff X1 and X2 have the same root."
  (= (ds-root disjoint-set x1) (ds-root disjoint-set x2)))

(declaim (inline find-argopt))
(defun find-argopt (vector predicate &key start end (key #'identity))
  (declare ((or null (integer 0 #.most-positive-fixnum)) start end)
           (vector vector))
  (labels ((invalid-range-error ()
             (error "Can't find optimal value in null interval [~A, ~A) on ~A" start end vector)))
    (let ((start (or start 0))
          (end (or end (length vector))))
      (when (or (>= start end)
                (>= start (length vector)))
        (invalid-range-error))
      (let ((opt-element (aref vector start))
            (opt-index start))
        (loop for i from start below end
              for x = (aref vector i)
              do (when (funcall predicate
                                (funcall key x i)
                                (funcall key opt-element i))
                   (setq opt-element x
                         opt-index i)))
        (values opt-index opt-element)))))


(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 main ()
  (declare #.OPT)
  (let* ((n (read))
         (d (read))
         (as (make-array n :element-type 'uint31))
         (edges (make-array (* 2 (sb-int:named-let recur ((l 0) (r n))
                                   (declare (uint31 l r)
                                            (values uint31 &optional))
                                   (if (<= (- r l) 1)
                                       0
                                       (let ((mid (ash (+ l r) -1)))
                                         (+ (- r l)
                                            (recur l mid)
                                            (recur mid r))))))
                            :element-type 'uint62))
         (end 0))
    (declare (uint31 n d end)
             ((simple-array uint62 (*)) edges))
    (dotimes (i n)
      (setf (aref as i) (read-fixnum)))
    (labels ((calc-cost (i j)
               (declare (uint31 i j)
                        (values uint62 &optional))
               (+ (aref as i) (aref as j)
                  (* d (abs (- i j))))))
      (sb-int:named-let recur ((l 0) (r n))
        (declare (uint31 l r))
        (when (>= (- r l) 2)
          (let ((mid (ash (+ l r) -1)))
            (recur l mid)
            (recur mid r)
            (let ((pivotl -1)
                  (minl most-positive-fixnum)
                  (pivotr -1)
                  (minr most-positive-fixnum))
              (loop for i from l below mid
                    for cost = (- (aref as i) (* d i))
                    when (<= cost minl)
                    do (setq pivotl i minl cost))
              (loop for i from mid below r
                    for cost = (+ (aref as i) (* d i))
                    when (<= cost minr)
                    do (setq pivotr i minr cost))
              (loop for i from l below mid
                    do (setf (aref edges end) (calc-cost i pivotr))
                       (incf end)
                       (setf (aref edges end) (dpb pivotr (byte 31 31) i))
                       (incf end))
              (loop for i from mid below r
                    do (setf (aref edges end) (calc-cost i pivotl))
                       (incf end)
                       (setf (aref edges end) (dpb pivotl (byte 31 31) i))
                       (incf end))))))
      (assert (= end (length edges)))
      (quicksort-by2! edges #'<)
      (let ((dset (make-disjoint-set n))
            (res 0))
        (declare (uint62 res))
        (loop for i from 0 below (length edges) by 2
              for cost = (aref edges i)
              for e = (aref edges (+ i 1))
              for v1 = (ldb (byte 31 0) e)
              for v2 = (ldb (byte 31 31) e)
              do (unless (ds-connected-p dset v1 v2)
                   (ds-unite! dset v1 v2)
                   (incf res cost)))
        (println res)))))

#-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 "3 1
1 100 1
"
    "106
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3 1000
1 100 1
"
    "2202
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "6 14
25 171 7 1 17 162
"
    "497
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "12 5
43 94 27 3 69 99 56 25 8 15 46 8
"
    "658
")))


Measured memory_bytes: 95588