(in-package :cl-user)
(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)

(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)

(defconstant +mod+ 1000000007)

(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)))

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

;; BEGIN_INSERTED_CONTENTS
(defpackage :cp/read-fixnum
  (:use :cl)
  (:export #:read-fixnum))
(in-package :cp/read-fixnum)

(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))))))))

(defpackage :cp/inverse-table
  (:use :cl)
  (:export #:make-inverse-table #:make-monotone-inverse-table!))
(in-package :cp/inverse-table)

(declaim (inline make-reverse-inverse-table))
(defun make-inverse-table (vector &key (test #'eql))
  "Returns a hash-table that assigns each value of the (usually sorted) VECTOR
of length n to the integers 0, ..., n-1."
  (let ((table (make-hash-table :test test :size (length vector))))
    (dotimes (i (length vector) table)
      (setf (gethash (aref vector i) table) i))))

(declaim (inline make-monotone-inverse-table!))
(defun make-monotone-inverse-table! (vector &key (test #'eql) (order #'<))
  "Sorts VECTOR, deletes all adjacent duplicates, and returns a hash-table that
assigns each value of the vector to the integers 0, 1, ..."
  (declare (function test order)
           (vector vector)
           (inline sort))
  (setq vector (sort vector order))
  (let ((table (make-hash-table :test test :size (length vector)))
        (index 0))
    (declare ((integer 0 #.most-positive-fixnum) index))
    (dotimes (pos (length vector))
      (when (or (zerop pos)
                (not (funcall test (aref vector pos) (aref vector (- pos 1)))))
        (setf (gethash (aref vector pos) table) index)
        (incf index)))
    (values table index)))

;;;
;;; 1-dimensional segment tree on arbitrary monoid (bottom-up implementation)
;;;

;; TODO: test
;; TODO: binary search

(defpackage :cp/abstract-segtree
  (:use :cl)
  (:export #:define-segtree))
(in-package :cp/abstract-segtree)

(defmacro define-segtree (name &key (operator '#'+) (identity 0) element-type)
  "OPERATOR := binary operator (comprising a monoid)
IDENTITY := object (identity element of the monoid)
ELEMENT-TYPE := type specifier

This macro defines three functions: <NAME>-REF, index-access function,
<NAME>-FOLD, query function for range sum, and MAKE-<NAME>, constructor."
  (let* ((fname-ref (intern (format nil "~A-REF" (symbol-name name))))
         (fname-fold (intern (format nil "~A-FOLD" (symbol-name name))))
         (fname-make (intern (format nil "MAKE-~A" (symbol-name name))))
         (fname-%make (intern (format nil "%MAKE-~A" (symbol-name name))))
         (fname-n (intern (format nil "%~A-N" (symbol-name name))))
         (fname-vector (intern (format nil "%~A-VECTOR" (symbol-name name))))
         (conc-name (intern (format nil "%~A-" (symbol-name name)))))
    `(progn
       (defstruct (,name (:constructor ,fname-%make
                             (vector &aux (n (ash (+ 1 (length vector)) -1))))
                         (:conc-name ,conc-name))
         (n nil :type (integer 0 #.(floor array-total-size-limit 2)))
         (vector nil :type (simple-array ,element-type (*))))
       (declaim (inline ,fname-make))
       (defun ,fname-make (size &key (initial-element ,identity) initial-contents)
         (declare ((integer 0 #.most-positive-fixnum) size)
                  ((or null sequence) initial-contents))
         (let ((res (make-array (- (* 2 size) 1)
                                :element-type ',element-type
                                :initial-element initial-element)))
           (when initial-contents
             (replace res initial-contents :start1 (- size 1)))
           (loop for i from (- size 2) downto 0
                 do (setf (aref res i)
                          (funcall ,operator
                                   (aref res (+ (* 2 i) 1)) (aref res (+ (* 2 i) 2)))))
           (,fname-%make res)))

       (declaim (inline ,fname-ref))
       (defun ,fname-ref (,name index)
         "Returns the element at INDEX."
         (declare ((integer 0 #.most-positive-fixnum) index))
         (aref (,fname-vector ,name)
               (+ index (,fname-n ,name) -1)))

       (declaim (inline (setf ,fname-ref)))
       (defun (setf ,fname-ref) (new-value ,name index)
         (declare ((integer 0 #.most-positive-fixnum) index)
                  (,element-type new-value))
         (let* ((vector (,fname-vector ,name))
                (i (+ index (- (,fname-n ,name) 1))))
           (declare ((integer 0 #.most-positive-fixnum) i))
           (setf (aref vector i) new-value)
           (loop while (> i 0)
                 do (setq i (ash (- i 1) -1))
                    (setf (aref vector i)
                          (funcall ,operator
                                   (aref vector (+ (* 2 i) 1))
                                   (aref vector (+ (* 2 i) 2)))))
           new-value))

       (declaim (inline ,fname-fold))
       (defun ,fname-fold (,name left right)
         "Folds the given half-open range [LEFT, RIGHT)."
         (declare ((integer 0 #.most-positive-fixnum) left right))
         (let* ((vector (,fname-vector ,name))
                (l (+ left (,fname-n ,name) -1))
                (r (+ right (,fname-n ,name) -1))
                (lvalue ,identity)
                (rvalue ,identity))
           (declare ((integer 0 #.most-positive-fixnum) l r)
                    (,element-type lvalue rvalue))
           (loop while (< l r)
                 when (evenp l)
                 do (setq lvalue (funcall ,operator lvalue (aref vector l)))
                    (incf l)
                 when (evenp r)
                 do (decf r)
                    (setq rvalue (funcall ,operator (aref vector r) rvalue))
                 do (setq l (ash (- l 1) -1)
                          r (ash (- r 1) -1)))
           (funcall ,operator lvalue rvalue))))))

#|

(define-segtree segtree
  :operator #'+
  :identity 0
  :element-type fixnum)

;|#

(defpackage :cp/modify-macro
  (:use :cl)
  (:export #:minf #:maxf #:mulf #:divf #:iorf #:xorf #:andf))
(in-package :cp/modify-macro)

(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))

;; BEGIN_USE_PACKAGE
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/modify-macro :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/abstract-segtree :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/inverse-table :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/read-fixnum :cl-user))
(in-package :cl-user)

;;;
;;; Body
;;;

(define-segtree segtree
  :operator #'max
  :identity 0
  :element-type uint31)

(declaim (ftype (function * (values (simple-array uint31 (*)) &optional)) calc-lis))
(defun calc-lis (as)
  (declare ((simple-array uint31 (*)) as))
  (let* ((n (length as))
         (dp (make-segtree n))
         (res (make-array n :element-type 'uint31 :initial-element 0)))
    (dotimes (i n)
      (let* ((a (aref as i))
             (max (segtree-fold dp 0 a)))
        (setf (aref res i) (+ max 1))
        (maxf (segtree-ref dp a) (+ max 1))))
    res))

(defun main ()
  (let* ((n (read))
         (as (make-array n :element-type 'uint31 :initial-element 0)))
    (dotimes (i n)
      (setf (aref as i) (read-fixnum)))
    (let ((inv-table (make-monotone-inverse-table! (copy-seq as))))
      (dotimes (i n)
        (setf (aref as i) (gethash (aref as i) inv-table)))
      (let ((max-a (reduce #'max as))
            (lis-left (calc-lis as))
            (lis-right (reverse (calc-lis (reverse as)))))
        (dotimes (i n)
          (setf (aref as i) (- max-a (aref as i))))
        (let ((lds-left (calc-lis as))
              (lds-right (reverse (calc-lis (reverse as))))
              (res 0))
          (loop for l across lis-left
                for r across lis-right
                do (maxf res (- (min l r) 1)))
          (loop for l across lds-left
                for r across lds-right
                do (maxf res (- (min l r) 1)))
          (println res))))))

#-swank (main)

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

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    #+os-windows (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)
    #+os-unix (run-program "xsel" '("-b" "-o") :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* (or out (make-string-output-stream)))
         (res (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))))))
    (if out res (get-output-stream-string *standard-output*))))

#+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
   (equal "1
"
          (run "3
1 3 2
" nil)))
  (it.bese.fiveam:is
   (equal "0
"
          (run "1
1
" nil)))
  (it.bese.fiveam:is
   (equal "2
"
          (run "6
5 3 1 2 4 2
" nil))))