(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 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))))

(eval-when (:compile-toplevel :load-toplevel :execute)
  (assert (= sb-vm:n-word-bits 64)))

(declaim (inline map-random-graph))
(defun map-random-graph (function n &optional (sample 1000))
  "Applies function SAMPLE times to the adjacency matrices of random directed
graphs of N vertices, which don't contain any multiple edges but may contain
self-loops.

If what you need is an undirected graph, you can just use the upper right (or
lower left) triangle. CANONIZE-ADJACENCY-MATRIX! may be helpful."
  (declare ((integer 1 #.most-positive-fixnum) n sample)
           (function function))
  (let* ((num-words (ceiling (* n n) sb-vm:n-word-bits))
         (matrix (make-array (list n n) :element-type 'bit :initial-element 0))
         (storage (array-storage-vector matrix)))
    (declare (optimize (speed 3) (safety 0)))
    (check-type num-words (integer 0 #.most-positive-fixnum))
    (dotimes (_ sample)
      (dotimes (i num-words)
        (setf (sb-kernel:%vector-raw-bits storage i) (random #.(expt 2 64))))
      (funcall function matrix))))

(declaim (inline canonize-adjacency-matrix!))
(defun canonize-adjacency-matrix! (matrix)
  "Removes self-loops and copies the right upper triangle to the left lower
triangle. This function destructively modifies the array."
  (let ((n (array-dimension matrix 0)))
    (dotimes (i n) (setf (aref matrix i i) 0))
    (dotimes (i n)
      (dotimes (j i)
        (setf (aref matrix i j) (aref matrix j i))))
    matrix))

(defun make-random-graph (size rate &optional directed)
  "Returns a adjacency-list representation of an random generated graph."
  (declare ((mod #.array-total-size-limit) size)
           ((real 0 1) rate))
  (let ((rate (float rate 1d0))
        (graph (make-array size :element-type 'list :initial-element nil)))
    (dotimes (i size)
      (if directed
          (loop for j from 0 below size
                when (and (/= i j)
                          (< (random 1d0) rate))
                do (push j (aref graph i)))
          (loop for j from (+ i 1) below size
                when (< (random 1d0) rate)
                do (push j (aref graph i))
                   (push i (aref graph j)))))
    graph))

(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 sample)
  (map-random-graph
   (lambda (mat)
     (canonize-adjacency-matrix! mat)
     (let ((sum (loop for j below n
                      when (= 1 (aref mat 0 j))
                      sum (+ j 1))))
       (when (and (not (zerop sum))
                  (loop for i from 1 below n
                        always (= (loop for j below n
                                        when (= 1 (aref mat i j))
                                        sum (+ j 1))
                                  sum)))
         (println-matrix mat)
         (terpri))))
   n
   sample))

;; n=5
;; 0 1 1 0 1
;; 1 0 0 1 1
;; 1 0 0 1 1
;; 0 1 1 0 1
;; 1 1 1 1 0
;; n=7
;; 0 1 1 1 1 0 1
;; 1 0 1 1 0 1 1
;; 1 1 0 0 1 1 1
;; 1 1 0 0 1 1 1
;; 1 0 1 1 0 1 1
;; 0 1 1 1 1 0 1
;; 1 1 1 1 1 1 0

;; n=6
;; 0 1 1 1 1 0
;; 1 0 1 1 0 1
;; 1 1 0 0 1 1
;; 1 1 0 0 1 1
;; 1 0 1 1 0 1
;; 0 1 1 1 1 0

;; n=8
;; 0 1 1 1 1 1 1 0
;; 1 0 1 1 1 1 0 1
;; 1 1 0 1 1 0 1 1
;; 1 1 1 0 0 1 1 1
;; 1 1 1 0 0 1 1 1
;; 1 1 0 1 1 0 1 1
;; 1 0 1 1 1 1 0 1
;; 0 1 1 1 1 1 1 0
(defun main ()
  (let* ((n (read))
         (mat (make-array (list n n) :element-type 'bit :initial-element 1)))
    (when (= n 3)
      (format t "2~%1 3~%2 3~%")
      (return-from main))
    (dotimes (i n)
      (setf (aref mat i i) 0))
    (let ((sum (if (evenp n) (- n 1) (- n 2))))
      (loop for i to sum
            do (setf (aref mat i (- sum i)) 0)))
    (println (floor (count 1 (array-storage-vector mat)) 2))
    (dotimes (i n)
      (loop for j from (+ i 1) below n
            when (= 1 (aref mat i j))
            do (format t "~D ~D~%" (+ i 1) (+ j 1))))))

#-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 "3
"
    "2
1 3
2 3
")))


Measured memory_bytes: 44384