(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
           #\# #\> (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 (inline shuffle!))
(defun shuffle! (vector &optional (start 0) end)
  "Destructively shuffles VECTOR by Fisher-Yates algorithm."
  (declare (vector vector)
           ((mod #.array-total-size-limit) start)
           ((or null (mod #.array-total-size-limit)) end))
  (loop for i from (- (or end (length vector)) 1) above start
        for j = (+ start (random (- (+ i 1) start)))
        do (rotatef (aref vector i) (aref vector j)))
  vector)

;;;
;;; Queue with singly linked list
;;;

(defstruct (queue (:constructor make-queue
                      (&optional list &aux (tail (last list)))))
  (list nil :type list)
  (tail nil :type list))

(declaim (inline enqueue))
(defun enqueue (obj queue)
  "Pushes OBJ to the end of QUEUE."
  (symbol-macrolet ((list (queue-list queue))
                    (tail (queue-tail queue)))
    (if (null list)
        (setf tail (list obj)
              list tail)
        (setf (cdr tail) (list obj)
              tail (cdr tail))))
  queue)

(declaim (inline dequeue))
(defun dequeue (queue)
  "Removes and returns the element at the front of QUEUE. Returns NIL if QUEUE
is empty."
  (pop (queue-list queue)))

(declaim (inline queue-empty-p))
(defun queue-empty-p (queue)
  (null (queue-list queue)))

(declaim (inline queue-peek))
(defun queue-peek (queue)
  (car (queue-list queue)))

(declaim (inline enqueue-front))
(defun enqueue-front (obj queue)
  "Pushes OBJ to the front of QUEUE."
  (symbol-macrolet ((list (queue-list queue))
                    (tail (queue-tail queue)))
    (if (null list)
        (setf tail (list obj)
              list tail)
        (push obj list))
    queue))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (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 #\-))
                                  (setq 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))))))))

(declaim (inline println-matrix))
(defun println-matrix (array &key (separator #\ ) (key #'identity) (writer #'write) (row-start 0) row-end (col-start 0) col-end)
  "Prints a 2-dimensional array."
  (declare ((array * (* *)) array)
           ((integer 0 #.most-positive-fixnum) row-start col-start))
  (let ((row-end (or row-end (array-dimension array 0)))
        (col-end (or col-end (array-dimension array 1))))
    (declare ((integer 0 #.most-positive-fixnum) row-end col-end))
    (loop for i from row-start below row-end
          do (loop for j from col-start below col-end
                   unless (= j col-start)
                   do (princ separator)
                   do (funcall writer (funcall key (aref array i j))))
             (terpri))))

(macrolet ((def (name fname)
             `(define-modify-macro ,name (new-value) ,fname)))
  (def minf min)
  (def maxf max)
  (def mulf *)
  (def divf /)
  (def iorf logior)
  (def xorf logxor)
  (def andf logand))

;;;
;;; Queue with singly linked list
;;;

(defstruct (queue (:constructor make-queue
                      (&optional list &aux (tail (last list)))))
  (list nil :type list)
  (tail nil :type list))

(declaim (inline enqueue))
(defun enqueue (obj queue)
  "Pushes OBJ to the end of QUEUE."
  (symbol-macrolet ((list (queue-list queue))
                    (tail (queue-tail queue)))
    (if (null list)
        (setf tail (list obj)
              list tail)
        (setf (cdr tail) (list obj)
              tail (cdr tail))))
  queue)

(declaim (inline dequeue))
(defun dequeue (queue)
  "Removes and returns the element at the front of QUEUE. Returns NIL if QUEUE
is empty."
  (pop (queue-list queue)))

(declaim (inline queue-empty-p))
(defun queue-empty-p (queue)
  (null (queue-list queue)))

(declaim (inline queue-peek))
(defun queue-peek (queue)
  (car (queue-list queue)))

(declaim (inline enqueue-front))
(defun enqueue-front (obj queue)
  "Pushes OBJ to the front of QUEUE."
  (symbol-macrolet ((list (queue-list queue))
                    (tail (queue-tail queue)))
    (if (null list)
        (setf tail (list obj)
              list tail)
        (push obj list))
    queue))

(in-package :cl-user)

(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 test (n seq)
  (let ((mat (make-array (list n n) :element-type 'uint32 :initial-element #xffffffff))
        (plan (make-array (list n n) :element-type 'bit :initial-element 0))
        (res 0))
    (labels ((%get (i j)
               ;; (dbg i j)
               (if (and (<= 0 i (- n 1))
                        (<= 0 j (- n 1)))
                   (aref mat i j)
                   0))
             (decode (p)
               (multiple-value-bind (quot rem) (floor (- p 1) n)
                 (values quot rem))))
      (sb-int:dovector (p (reverse seq))
        (multiple-value-bind (i j) (decode p)
          (setf (aref plan i j) 1))
        (fill (array-storage-vector mat) #xffffffff)
        (dotimes (_ (* n n))
          (dotimes (i n)
            (dotimes (j n)
              (let ((res (min (%get (- i 1) j)
                              (%get (+ i 1) j)
                              (%get i (- j 1))
                              (%get i (+ j 1)))))
                (if (= (aref plan i j) 1)
                    (minf (aref mat i j) (+ res 1))
                    (minf (aref mat i j) res))))))
        (multiple-value-bind (i j) (decode p)
          (setf (aref plan i j) 1)
          (incf res (- (aref mat i j) 1)))
        ;; (println-matrix mat)
        )
      res)))

(defun bench (n sample)
  (loop repeat sample
        do (let ((vec (make-array (* n n) :element-type 'uint31)))
             (dotimes (i (* n n))
               (setf (aref vec i) (+ i 1)))
             (shuffle! vec)
             (assert (= (test n vec) (solve n vec))))))

(defun solve (n ps)
  (declare #.OPT
           (uint16 n)
           ((simple-array uint31 (*)) ps))
  (let* (;; 0-bit: up, 1: down, 2: left, 3: right
         (dists (make-array '(500 500) :element-type 'uint8 :initial-element 0))
         (plan (make-array '(500 500) :element-type 'bit :initial-element 1))
         (que (make-queue))
         (res 0))
    (declare (uint16 n)
             (uint32 res))
    (dotimes (i (* n n))
      (setf (aref ps i) (- (aref ps i) 1)))
    (dotimes (i n)
      (dotimes (j n)
        (setf (aref dists i j)
              (min (+ i 1) (+ j 1) (- n i) (- n j)))))
    (labels ((decode (p) (floor p n))
             (visit (new-i new-j prev-dist)
               (declare (int32 new-i new-j prev-dist))
               (when (and (<= 0 new-i (- n 1))
                          (<= 0 new-j (- n 1)))
                 (let ((new-dist (+ prev-dist (aref plan new-i new-j))))
                   (when (< new-dist (aref dists new-i new-j))
                     (setf (aref dists new-i new-j) new-dist)
                     (enqueue (cons new-i new-j) que))))))
      (sb-int:dovector (p ps)
        (multiple-value-bind (i j) (decode p)
          (decf (aref dists i j))
          (incf res (aref dists i j))
          (setf (aref plan i j) 0)
          (enqueue (cons i j) que)
          (loop until (queue-empty-p que)
                for (i . j) = (dequeue que)
                for dist = (aref dists i j)
                do (visit (- i 1) j dist)
                   (visit (+ i 1) j dist)
                   (visit i (- j 1) dist)
                   (visit i (+ j 1) dist))))
      res)))

(defun main ()
  (let* ((n (read))
         (ps (make-array (* n n) :element-type 'uint31 :initial-element 0)))
    (dotimes (i (* n n))
      (setf (aref ps i) (read-fixnum)))
    (println (solve n ps))))

#-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 "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 "500~%")
    (let ((vec (make-array (* 500 500))))
      (dotimes (i (* 500 500))
        (setf (aref vec i) (+ i 1)))
      (shuffle! vec)
      (dotimes (i (* 500 500))
        (println (aref vec i) 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 3 7 9 5 4 8 6 2
"
    "1
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "4
6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8
"
    "3
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "6
11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30
"
    "11
")))


Measured memory_bytes: 86208