Problem:
Score : 500 points

Problem Statement

Snuke has a string s.
From this string, Anuke, Bnuke, and Cnuke obtained strings a, b, and c, respectively, as follows:

Choose a non-empty (contiguous) substring of s (possibly s itself). Then, replace some characters (possibly all or none) in it with ?s.

For example, if s is mississippi, we can choose the substring ssissip and replace its 1-st and 3-rd characters with ? to obtain ?s?ssip.

You are given the strings a, b, and c.
Find the minimum possible length of s.

Constraints

1 \leq |a|, |b|, |c| \leq 2000

a, b, and c consists of lowercase English letters and ?s.

Input

Input is given from Standard Input in the following format:

a
b
c

Output

Print the minimum possible length of s.

Sample Input 1

a?c
der
cod

Sample Output 1

7

For example, s could be atcoder.

Sample Input 2

atcoder
atcoder
???????

Sample Output 2

7

a, b, and c may not be distinct.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(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
(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 solve (a b c)
  (declare #.OPT
           (simple-base-string a b c))
  (let ((len-a (length a))
        (len-b (length b))
        (len-c (length c))
        (min #xffffffff))
    (declare (uint32 len-a len-b len-c min))
    (dotimes (init1 (+ len-a 1))
      (block outer
        (loop for i from init1 below len-a
              for j from 0 below len-b
              unless (or (char= (aref a i) (aref b j))
                         (char= (aref a i) #\?)
                         (char= (aref b j) #\?))
              do (return-from outer)
              finally
                 (let ((ab (make-string (max len-a (+ init1 len-b))
                                        :element-type 'base-char)))
                   (dotimes (i len-a)
                     (setf (aref ab i) (aref a i)))
                   (loop for j below len-b
                         for i = (+ j init1)
                         do (cond ((>= i len-a)
                                   (setf (aref ab i) (aref b j)))
                                  ((char= #\? (aref a i) (aref b j))
                                   (setf (aref ab i) #\?))
                                  ((char= #\? (aref a i))
                                   (setf (aref ab i) (aref b j)))
                                  ((char= #\? (aref b j))
                                   (setf (aref ab i) (aref a i)))
                                  (t
                                   (assert (char= (aref a i) (aref b j)))
                                   (setf (aref ab i) (aref b j)))))
                   (dbg init1 ab)
                   (let ((len-ab (length ab)))
                     (dotimes (init2 (+ len-ab 1))
                       (when (>= (max len-ab (+ init2 len-c)) min)
                         (return))
                       (block inner
                         (loop for i from init2 below len-ab
                               for j from 0 below len-c
                               unless (or (char= (aref ab i) (aref c j))
                                          (char= (aref ab i) #\?)
                                          (char= (aref c j) #\?))
                               do (return-from inner)
                               finally (setq min (min min (max len-ab (+ init2 len-c))))))))))))
    min))

(defun main ()
  (let* ((a (coerce (read-line) 'simple-base-string))
         (b (coerce (read-line) 'simple-base-string))
         (c (coerce (read-line) 'simple-base-string)))
    ;; (solve b a c)
    (println
     (min (solve a b c)
          (solve a c b)
          (solve b c a)
          (solve b a c)
          (solve c a b)
          (solve c b a)))
    ))

#-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 "")))

#+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 "a?c
der
cod
"
    "7
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "atcoder
atcoder
???????
"
    "7
")))