Problem:
Score: 600 points

Problem Statement

There is a grass field that stretches infinitely.

In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).

There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).

What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.

Constraints

All values in input are integers between -10^9 and 10^9 (inclusive).

1 \leq N, M \leq 1000

A_i < B_i\ (1 \leq i \leq N)

E_j < F_j\ (1 \leq j \leq M)

The point (0, 0) does not lie on any of the given segments.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M

Output

If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \mathrm{cm^2}.

(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)

Sample Input 1

5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4

Sample Output 1

13

The area of the region the cow can reach is 13\ \mathrm{cm^2}.

Sample Input 2

6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4

Sample Output 2

INF

The area of the region the cow can reach is infinite.

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Wrong Answer)

#-swank
(unless (member :child-sbcl *features*)
  (quit
   :unix-status
   (process-exit-code
    (run-program *runtime-pathname*
                 `("--control-stack-size" "256MB"
                   "--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
                   "--eval" "(push :child-sbcl *features*)"
                   "--script" ,(namestring *load-pathname*))
                 :output t :error t :input t))))
(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 bisect-left))
(defun bisect-left (target value &key (start 0) end (order #'<) (key #'identity))
  "TARGET := vector | function (taking an integer argument)
ORDER := strict order

Analogue of lower_bound() of C++ or bisect_left() of Python: Returns the
smallest index (or input) i that fulfills TARGET[i] >= VALUE, where '>=' is the
complement of ORDER. In other words, this function returns the leftmost index at
which VALUE can be inserted with keeping the order. Therefore, TARGET must be
monotonically non-decreasing with respect to ORDER.

- This function returns END if VALUE exceeds TARGET[END-1]. 
- The range [START, END) is half-open.
- END must be explicitly specified if TARGET is function.
- KEY is applied to each element of TARGET before comparison."
  (declare (function key order)
           (integer start)
           ((or null integer) end))
  (macrolet
      ((frob (accessor &optional declaration)
         `(labels
              ((%bisect-left (ng ok)
                 ;; TARGET[OK] >= VALUE always holds (assuming
                 ;; TARGET[END] = +infinity)
                 ,@(when declaration (list declaration))
                 (if (<= (- ok ng) 1)
                     ok
                     (let ((mid (ash (+ ng ok) -1)))
                       (if (funcall order (funcall key (,accessor target mid)) value)
                           (%bisect-left mid ok)
                           (%bisect-left ng mid))))))
            (assert (<= start end))
            (%bisect-left (- start 1) end))))
    (etypecase target
      (vector
       (let ((end (or end (length target))))
         (frob aref (declare ((integer -1 (#.most-positive-fixnum)) ng ok)))))
      (function
       (assert end () "Requires END argument if TARGET is a function.")
       (frob funcall)))))

(declaim (inline bisect-right))
(defun bisect-right (target value &key (start 0) end (order #'<) (key #'identity))
  "TARGET := vector | function (taking an integer argument)
ORDER := strict order

Analogue of upper_bound() of C++ or bisect_right() of Python: Returns the
smallest index (or input) i that fulfills TARGET[i] > VALUE. In other words,
this function returns the rightmost index at which VALUE can be inserted with
keeping the order. Therefore, TARGET must be monotonically non-decreasing with
respect to ORDER.

- This function returns END if VALUE >= TARGET[END-1].
- The range [START, END) is half-open.
- END must be explicitly specified if TARGET is function.
- KEY is applied to each element of TARGET before comparison."
  (declare (function key order)
           (integer start)
           ((or null integer) end))
  (macrolet
      ((frob (accessor &optional declaration)
         `(labels
              ((%bisect-right (ng ok)
                 ;; TARGET[OK] > VALUE always holds (assuming
                 ;; TARGET[END] = +infinity)
                 ,@(when declaration (list declaration))
                 (if (<= (- ok ng) 1)
                     ok
                     (let ((mid (ash (+ ng ok) -1)))
                       (if (funcall order value (funcall key (,accessor target mid)))
                           (%bisect-right ng mid)
                           (%bisect-right mid ok))))))
            (assert (<= start end))
            (%bisect-right (- start 1) end))))
    (etypecase target
      (vector
       (let ((end (or end (length target))))
         (frob aref (declare ((integer -1 (#.array-total-size-limit)) ng ok)))))
      (function
       (assert end () "Requires END argument if TARGET is a function.")
       (frob funcall)))))

;;;
;;; Sort multiple vectors
;;;

;; TODO: throw an error if there are two ore more identical vectors in the given
;; vectors

(declaim (inline %median3))
(defun %median3 (x y z order)
  (if (funcall order x y)
      (if (funcall order y z)
          y
          (if (funcall order z x)
              x
              z))
      (if (funcall order z y)
          y
          (if (funcall order x z)
              x
              z))))

(defun parallel-sort! (vector order &rest vectors)
  "Destructively sorts VECTOR w.r.t. ORDER and applies the same permutation to
all the vectors in VECTORS.

Note: not randomized; shuffle the inputs if necessary"
  (declare (vector vector))
  (labels
      ((recur (left right)
         (when (< left right)
           (let* ((l left)
                  (r right)
                  (pivot (%median3 (aref vector l)
                                   (aref vector (ash (+ l r) -1))
                                   (aref vector r)
                                   order)))
             (declare ((integer 0 #.most-positive-fixnum) l r))
             (loop (loop while (funcall order (aref vector l) pivot)
                         do (incf l 1))
                   (loop while (funcall order pivot (aref vector r))
                         do (decf r 1))
                   (when (>= l r)
                     (return))
                   (rotatef (aref vector l) (aref vector r))
                   (dolist (v vectors)
                     (rotatef (aref v l) (aref v r)))
                   (incf l 1)
                   (decf r 1))
             (recur left (- l 1))
             (recur (+ r 1) right)))))
    (recur 0 (- (length vector) 1))
    vector))

#+sbcl
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-c:define-source-transform parallel-sort! (vector order &rest vectors)
    (let ((vec (gensym))
          (vecs (loop for _ in vectors collect (gensym))))
      `(let ((,vec ,vector)
             ,@(loop for v in vectors
                     for sym in vecs
                     collect `(,sym ,v)))
         (labels
             ((recur (left right)
                (when (< left right)
                  (let* ((l left)
                         (r right)
                         (pivot (%median3 (aref ,vec l)
                                          (aref ,vec (ash (+ l r) -1))
                                          (aref ,vec r)
                                          ,order)))
                    (declare ((integer 0 #.most-positive-fixnum) l r))
                    (loop (loop while (funcall ,order (aref ,vec l) pivot)
                                do (incf l 1))
                          (loop while (funcall ,order pivot (aref ,vec r))
                                do (decf r 1))
                          (when (>= l r)
                            (return))
                          (rotatef (aref ,vec l) (aref ,vec r))
                          ,@(loop for sym in vecs
                                  collect `(rotatef (aref ,sym l) (aref ,sym r)))
                          (incf l 1)
                          (decf r 1))
                    (recur left (- l 1))
                    (recur (+ r 1) right)))))
           (recur 0 (- (length ,vec) 1))
           ,vec)))))

(defun parallel-shuffle! (vector &rest vectors)
   "Destructively shuffles VECTOR and applies the same permutation to all the
vectors in VECTORS."
  (loop for i from (- (length vector) 1) above 0
        for j = (random (+ i 1))
        do (rotatef (aref vector i) (aref vector j))
           (dolist (v vectors)
             (rotatef (aref v i) (aref v j)))
        finally (return vector)))

#+sbcl
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-c:define-source-transform parallel-shuffle! (vector &rest vectors)
    (let ((vec (gensym))
          (vecs (loop for _ in vectors collect (gensym))))
      `(let ((,vec ,vector)
             ,@(loop for v in vectors
                     for sym in vecs
                     collect `(,sym ,v)))
         (loop for i from (- (length ,vec) 1) above 0
               for j = (random (+ i 1))
               do (rotatef (aref ,vec i) (aref ,vec j))
                  ,@(loop for sym in vecs
                          collect `(rotatef (aref ,sym i) (aref ,sym j)))
               finally (return ,vec))))))

(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
;;;

(defconstant +neg-inf+ #x-80000000)
(defconstant +pos-inf+ #x7fffffff)
(defun main ()
  (let* ((n (read))
         (m (read))
         (as (make-array (+ n 2) :element-type 'int32 :initial-element 0))
         (bs (make-array (+ n 2) :element-type 'int32 :initial-element 0))
         (cs (make-array (+ n 2) :element-type 'int32 :initial-element 0))
         (ds (make-array (+ m 2) :element-type 'int32 :initial-element 0))
         (es (make-array (+ m 2) :element-type 'int32 :initial-element 0))
         (fs (make-array (+ m 2) :element-type 'int32 :initial-element 0))
         (graph (make-array (* (+ n 1) (+ m 1)) :element-type 'list :initial-element nil)))
    (labels ((to-idx (i j) (+ i (* j (+ n 1))))
             (rev (idx)
               (multiple-value-bind (quot rem) (floor idx (+ n 1))
                 (values rem quot))))
      (dotimes (i n)
        (setf (aref as i) (read)
              (aref bs i) (read)
              (aref cs i) (read)))
      (setf (aref cs n) +neg-inf+
            (aref cs (+ n 1)) +pos-inf+)
      (dotimes (i m)
        (setf (aref ds i) (read)
              (aref es i) (read)
              (aref fs i) (read)))
      (setf (aref ds m) +neg-inf+
            (aref ds (+ m 1)) +pos-inf+)
      (parallel-sort! cs #'< as bs)
      (parallel-sort! ds #'< es fs)
      (loop
        for i from 0 to n
        do (loop
             for j from 0 to m
             do (let ((d1 (aref ds j))
                      (d2 (aref ds (+ j 1))))
                  (when (< i n)
                    (let ((a (aref as (+ i 1)))
                          (b (aref bs (+ i 1))))
                      (unless (<= a d1 d2 b)
                        (push (to-idx (+ i 1) j) (aref graph (to-idx i j))))))
                  (when (> i 0)
                    (let ((a (aref as i))
                          (b (aref bs i)))
                      (unless (<= a d1 d2 b)
                        (push (to-idx (- i 1) j) (aref graph (to-idx i j)))))))
                (let ((c1 (aref cs i))
                      (c2 (aref cs (+ i 1))))
                  (when (< j m)
                    (let ((e (aref es (+ j 1)))
                          (f (aref fs (+ j 1))))
                      (unless (<= e c1 c2 f)
                        (push (to-idx i (+ j 1)) (aref graph (to-idx i j))))))
                  (when (> j 0)
                    (let ((e (aref es j))
                          (f (aref fs j)))
                      (unless (<= e c1 c2 f)
                        (push (to-idx i (- j 1)) (aref graph (to-idx i j)))))))))
      (let* ((init-i (- (bisect-left cs 0) 1))
             (init-j (- (bisect-left ds 0) 1))
             (init (to-idx init-i init-j))
             (marked (make-array (* (+ n 1) (+ m 1)) :element-type 'bit :initial-element 0)))
        (sb-int:named-let dfs ((v init))
          (setf (aref marked v) 1)
          (dolist (next (aref graph v))
            (when (zerop (aref marked next))
              (dfs next))))
        (let ((res 0))
          (dotimes (idx (length marked))
            (when (= 1 (aref marked idx))
              (multiple-value-bind (i j) (rev idx)
                (let ((c1 (aref cs i))
                      (c2 (aref cs (+ i 1)))
                      (d1 (aref ds j))
                      (d2 (aref ds (+ j 1))))
                  (incf res (* (- c2 c1) (- d2 d1)))))))
          (when (and (loop for i to n always (= 1 (aref marked (to-idx i 0))))
                     (loop for i to n always (= 1 (aref marked (to-idx i m))))
                     (loop for j to m always (= 1 (aref marked (to-idx 0 j))))
                     (loop for j to m always (= 1 (aref marked (to-idx n j)))))
            (write-line "INF")
            (return-from main))
          (println 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 "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 "5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4
"
    "13
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4
"
    "INF
")))