;; -*- coding: utf-8 -*-
(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)) (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 map-indices))
(defun map-indices (function max-indices)
  "Applies function to each vector of indices smaller than MAX-INDICES. The
consequence is undefined when the vector is modified in FUNCTION."
  (declare ((simple-array (unsigned-byte 8) (*)) max-indices))
  (let* ((size (length max-indices))
         (indices (make-array size :element-type '(unsigned-byte 8))))
    (labels ((recur (pos)
               (declare ((integer 0 #.array-dimension-limit) pos))
               (if (= pos size)
                   (funcall function indices)
                   (dotimes (idx (the (integer 0 #.most-positive-fixnum)
                                      (aref max-indices pos)))
                     (setf (aref indices pos) idx)
                     (recur (+ pos 1))))))
      (recur 0))))

(defmacro do-indices ((var end-indices) &body body)
  "DO-style macro for MAP-INDICES"
  `(block nil (map-indices (lambda (,var) ,@body) ,end-indices)))

(declaim (ftype (function * (values simple-bit-vector &optional)) make-prime-table))
(defun make-prime-table (sup)
  "Returns a simple-bit-vector of length SUP, whose (0-based) i-th bit is 1 if i
is prime and 0 otherwise.

Example: (make-prime-table 10) => #*0011010100"
  (declare (optimize (speed 3) (safety 0)))
  (check-type sup (integer 2 (#.array-total-size-limit)))
  (let ((table (make-array sup :element-type 'bit :initial-element 0))
        (sup/64 (ceiling sup 64)))
    ;; special treatment for p = 2
    (dotimes (i sup/64)
      (setf (sb-kernel:%vector-raw-bits table i) #xAAAAAAAAAAAAAAAA))
    (setf (sbit table 1) 0
          (sbit table 2) 1)
    ;; p >= 3
    (loop for p from 3 to (+ 1 (isqrt (- sup 1))) by 2
          when (= 1 (sbit table p))
          do (loop for composite from (* p p) below sup by p
                   do (setf (sbit table composite) 0)))
    table))

;; FIXME: Currently the element type of the resultant vector is (UNSIGNED-BYTE 62).
(defun make-prime-sequence (sup)
  "Returns the ascending sequence of primes smaller than SUP."
  (declare (optimize (speed 3) (safety 0)))
  (check-type sup (integer 2 (#.array-total-size-limit)))
  (let ((table (make-prime-table sup)))
    (let* ((length (count 1 table))
           (result (make-array length :element-type '(integer 0 #.most-positive-fixnum)))
           (index 0))
      (declare ((integer 0 #.most-positive-fixnum) length))
      (loop for x below sup
            when (= 1 (sbit table x))
            do (setf (aref result index) x)
               (incf index))
      (values result table))))

(defstruct (prime-data (:constructor %make-prime-data (seq table)))
  (seq nil :type (simple-array (integer 0 #.most-positive-fixnum) (*)))
  (table nil :type simple-bit-vector))

(defun make-prime-data (sup)
  (multiple-value-call #'%make-prime-data (make-prime-sequence sup)))

(declaim (inline factorize)
         (ftype (function * (values list &optional)) factorize))
(defun factorize (x prime-data)
  "Returns the associative list of prime factors of X, which is composed
of (<prime> . <exponent>). E.g. (factorize 100 <prime-table>) => '((2 . 2) (5
. 5)).

- Any numbers beyond the range of PRIME-DATA are regarded as prime.
- The returned list is in descending order w.r.t. prime factors."
  (declare (integer x))
  (setq x (abs x))
  (when (<= x 1)
    (return-from factorize nil))
  (let ((prime-seq (prime-data-seq prime-data))
        result)
    (loop for prime of-type unsigned-byte across prime-seq
          do (when (= x 1)
               (return-from factorize result))
             (loop for exponent of-type (integer 0 #.most-positive-fixnum) from 0
                   do (multiple-value-bind (quot rem) (floor x prime)
                        (if (zerop rem)
                            (setf x quot)
                            (progn
                              (when (> exponent 0)
                                (push (cons prime exponent) result))
                              (loop-finish))))))
    (if (= x 1)
        result
        (cons (cons x 1) result))))

(defun make-omega-table (sup prime-data)
  "Returns the table of prime omega function on {0, 1, ..., SUP-1}."
  (declare ((integer 0 #.most-positive-fixnum) sup))
  ;; (assert (>= (expt (aref prime-seq (- (length prime-seq) 1)) 2) (- sup 1)))
  (let ((prime-seq (prime-data-seq prime-data))
        (table (make-array sup :element-type '(unsigned-byte 32)))
        (res (make-array sup :element-type '(unsigned-byte 8))))
    (dotimes (i (length table))
      (setf (aref table i) i))
    (loop for p of-type (integer 0 #.most-positive-fixnum) across prime-seq
          do (loop for i from p below sup by p
                   do (loop
                        (multiple-value-bind (quot rem) (floor (aref table i) p)
                          (if (zerop rem)
                              (progn (incf (aref res i))
                                     (setf (aref table i) quot))
                              (return))))))
    (loop for i below sup
          unless (= 1 (aref table i))
          do (incf (aref res i)))
    res))

(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
;;;

(define-modify-macro maxf (new-value) max)
(defun main ()
  (declare #.OPT)
  (let* ((pdata (make-prime-data 10001))
         (n (read))
         (as (make-array n :element-type 'uint31))
         (pfactors (make-array n :element-type 'list :initial-element 0))
         (lcmfactors (make-hash-table)))
    (dotimes (i n)
      (let ((a (read)))
        (setf (aref as i) a)
        (setf (aref pfactors i) (factorize a pdata))))
    (sb-int:dovector (pfactor pfactors)
      (dolist (node pfactor)
        (let ((p (car node))
              (count (cdr node)))
          (if (gethash p lcmfactors)
              (maxf (gethash p lcmfactors) count)
              (setf (gethash p lcmfactors) count)))))
    (let* ((count (hash-table-count lcmfactors))
           (ps (make-array count :element-type 'uint32))
           (counts (make-array count :element-type 'uint8))
           (pos 0)
           (res 0))
      (sb-int:dohash ((p count) lcmfactors)
        (setf (aref ps pos) p
              (aref counts pos) 2)
        (incf pos))
      (let ((init t))
        (do-indices (seq counts)
          (if init
              (setq init nil)
              (let ((parity (reduce #'+ seq))
                    (divisor 1))
                (declare (uint62 divisor))
                (loop for c across seq
                      for p across ps
                      when (= c 1)
                      do (setq divisor (the uint62 (* divisor p))))
                ;; #>divisor
                (let* ((count (count-if (lambda (x) (declare (uint62 x)) (zerop (mod x divisor))) as))
                       (value (- (expt 2 count) 1)))
                  ;; #>value
                  (if (oddp parity)
                      (incf res value)
                      (decf res value)))))))
      (println (- (expt 2 n) 1 res)))))

#-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 "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))

#+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)))