;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (ql:quickload '(:cl-debug-print :fiveam))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(declaim (inline tzcount))
(defun tzcount (x)
  "Is equivalent to TZCNT operation: it returns the number of trailing zero
bits. Note that (TZCOUNT 0) = -1."
  (- (integer-length (logand x (- x))) 1))

;;;
;;; Memoization macro
;;;

;; TODO: detailed documentation

;; Usage example:
;; (with-cache (:hash-table :test #'equal :key #'cons)
;;   (defun ...))
;; (with-cache (:array (10 10 * 10) :initial-element -1 :element-type 'fixnum)
;;   (defun foo (a b c d) ...)) ; => C is ignored.
;; (with-cache (:array (10 10) :initial-element -1 :element-type 'fixnum :debug t)
;;   (defun foo (x y) ...)) ; executes with trace of foo

;; FIXME: *RECURSION-DEPTH* should be included within the macro.
(declaim (type (integer 0 #.most-positive-fixnum) *recursion-depth*))
(defparameter *recursion-depth* 0)

(defmacro with-cache (cache-attribs def-form)
  (let* ((cache-attribs (if (atom cache-attribs) (list cache-attribs) cache-attribs))
         (cache-type (first cache-attribs))
         (dimensions-with-* (when (eql cache-type :array) (second cache-attribs)))
         (dimensions (remove '* dimensions-with-*))
         (rank (length dimensions))
         (rest-attribs (ecase cache-type
                         (:hash-table (cdr cache-attribs))
                         (:array (cddr cache-attribs))))
         (key (prog1 (getf rest-attribs :key) (remf rest-attribs :key)))
         (debug (prog1 (getf rest-attribs :debug) (remf rest-attribs :debug)))
         (cache-form (case cache-type
                       (:hash-table `(make-hash-table ,@rest-attribs))
                       (:array `(make-array (list ,@dimensions) ,@rest-attribs))))
         (initial-element (when (eql cache-type :array)
                            (assert (member :initial-element rest-attribs))
                            (getf rest-attribs :initial-element))))
    (let ((cache (gensym))
          (value (gensym))
	  (present-p (gensym))
          (name-alias (gensym))
	  (args-lst (gensym))
          (indices (loop repeat rank collect (gensym))))
      (labels ((debug (name args obj)
                 (let ((value (gensym)))
                   (if debug
                       `(progn
                          (format t "~&~A~A: (~A ~{~A~^ ~}) =>"
                                  (make-string *recursion-depth*
                                               :element-type 'base-char
                                               :initial-element #\ )
                                  *recursion-depth*
                                  ',name
                                  (list ,@args))
                          (let ((,value (let ((*recursion-depth* (1+ *recursion-depth*)))
                                          ,obj)))
                            (format t "~&~A~A: (~A ~{~A~^ ~}) => ~A"
                                    (make-string *recursion-depth*
                                                 :element-type 'base-char
                                                 :initial-element #\ )
                                    *recursion-depth*
                                    ',name
                                    (list ,@args)
                                    ,value)
                            ,value))
                       obj)))
               (make-cache-check-form (cache-type name args)
                 (debug name
                        args
                        (case cache-type
                          (:hash-table
                           `(let ((,args-lst (funcall ,(or key #'list) ,@args)))
                              (multiple-value-bind (,value ,present-p)
                                  (gethash ,args-lst ,cache)
                                (if ,present-p
                                    ,value
                                    (setf (gethash ,args-lst ,cache)
                                          (,name-alias ,@args))))))
                          (:array
                           (let ((memoized-args (loop for dimension in dimensions-with-*
                                                      for arg in args
                                                      unless (eql dimension '*)
                                                      collect arg)))
                             (if key
                                 `(multiple-value-bind ,indices
                                      (funcall ,key ,@memoized-args)
                                    (let ((,value (aref ,cache ,@indices)))
                                      (if (eql ,initial-element ,value)
                                          (setf (aref ,cache ,@indices)
                                                (,name-alias ,@args))
                                          ,value)))
                                 `(let ((,value (aref ,cache ,@memoized-args)))
                                    (if (eql ,initial-element ,value)
                                        (setf (aref ,cache ,@memoized-args)
                                              (,name-alias ,@args))
                                        ,value))))))))
               (make-reset-form (cache-type)
                 (case cache-type
                   (:hash-table `(setf ,cache (make-hash-table ,@rest-attribs)))
                   (:array `(prog1 nil
                              (fill (array-storage-vector ,cache) ,initial-element)))))
               (make-reset-name (name)
                 (intern (format nil "RESET-~A" (symbol-name name))))
               (extract-declarations (body)
                 (remove-if-not (lambda (form) (eql 'declare (car form))) body)))
        (ecase (car def-form)
          ((defun)
           (destructuring-bind (_ name args &body body) def-form
             (declare (ignore _))
             `(let ((,cache ,cache-form))
                (defun ,(make-reset-name name) () ,(make-reset-form cache-type))
                (defun ,name ,args
                  ,@(extract-declarations body)
                  (labels ((,name-alias ,args ,@body))
                    (declare (inline ,name-alias))
                    ,(make-cache-check-form cache-type name args))))))
          ((nlet #+sbcl sb-int:named-let)
           (destructuring-bind (_ name bindings &body body) def-form
             (declare (ignore _))
             `(let ((,cache ,cache-form))
                (,(car def-form) ,name ,bindings
                 ,@(extract-declarations body)
                 ,(let ((args (mapcar (lambda (x) (if (atom x) x (car x))) bindings)))
                    `(labels ((,name-alias ,args ,@body))
                       (declare (inline ,name-alias))
                       ,(make-cache-check-form cache-type name args)))))))
          ((labels flet)
           (destructuring-bind (_ definitions &body labels-body) def-form
             (declare (ignore _))
             (destructuring-bind (name args &body body) (car definitions)
               `(let ((,cache ,cache-form))
                  (,(car def-form)
                   ((,(make-reset-name name) () ,(make-reset-form cache-type))
                    (,name ,args
                           ,@(extract-declarations body)
                           (labels ((,name-alias ,args ,@body))
                             (declare (inline ,name-alias))
                             ,(make-cache-check-form cache-type name args)))
                    ,@(cdr definitions))
                   (declare (ignorable #',(make-reset-name name)))
                   ,@labels-body))))))))))

(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))
         (as (make-array (list n n) :element-type 'int32))
         (alls (make-array (ash 1 n) :element-type 'fixnum)))
    (declare ((integer 1 16) n))
    (dotimes (i n)
      (dotimes (j n)
        (setf (aref as i j) (read))))
    (dotimes (bits (ash 1 n))
      (let ((score 0)
            (lo (tzcount bits))
            (hi (integer-length bits)))
        (declare (fixnum score lo hi))
        (loop for pos1 from (max 0 lo) below hi
              do (loop for pos2 from (+ pos1 1) below hi
                       when (and (logbitp pos1 bits)
                                 (logbitp pos2 bits))
                       do (incf score (aref as pos1 pos2))))
        (setf (aref alls bits) score)))
    (with-cache (:array ((ash 1 n)) :element-type 'fixnum :initial-element most-negative-fixnum)
      (labels ((recur (bits)
                 (if (zerop bits)
                     0
                     (let ((res (aref alls bits)))
                       (declare (fixnum res))
                       (do ((subs (logand (- bits 1) bits)
                                  (logand (- subs 1) bits)))
                           ((zerop subs))
                         ;; (format t "~B ~B ~B~%" bits subs (logxor bits subs))
                         (setq res (max res
                                        (+ (recur subs)
                                           (recur (logxor bits subs))))))
                       res))))
        (println (recur (- (ash 1 n) 1)))))))

#-swank (main)


Measured memory_bytes: 19432