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: Accepted)

#-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
(macrolet ((def (name fname)
             `(define-modify-macro ,name (new-value) ,fname)))
  (def minf min)
  (def maxf max)
  (def mulf *)
  (def divf /)
  (def iorf logior)
  (def xorf logxor)
  (def andf logand))

(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 solve (n m as bs cs ds es fs)
  (declare #.OPT
           (uint31 n m)
           ((simple-array int32 (*)) as bs cs ds es fs))
  (let* ((init-i (- (position-if (lambda (c) (>= c 0)) cs) 1))
         (init-j (- (position-if (lambda (d) (>= d 0)) ds) 1))
         (marked (make-array '(1001 1001) :element-type 'bit :initial-element 0)))
    (sb-int:named-let dfs ((i init-i) (j init-j))
      (when (zerop (aref marked i j))
        (setf (aref marked i j) 1)
        (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)
                (dfs (+ i 1) j))))
          (when (> i 0)
            (let ((a (aref as i))
                  (b (aref bs i)))
              (unless (<= a d1 d2 b)
                (dfs (- i 1) 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)
                (dfs i (+ j 1)))))
          (when (> j 0)
            (let ((e (aref es j))
                  (f (aref fs j)))
              (unless (<= e c1 c2 f)
                (dfs i (- j 1))))))))
    (when (and (loop for i to n always (= 1 (aref marked i 0)))
               (loop for i to n always (= 1 (aref marked i m)))
               (loop for j to m always (= 1 (aref marked 0 j)))
               (loop for j to m always (= 1 (aref marked n j))))
      (return-from solve nil))
    (let ((res 0))
      (declare (int64 res))
      (dotimes (i n)
        (dotimes (j m)
          (when (= 1 (aref marked i j))
            (let ((c1 (aref cs i))
                  (c2 (aref cs (+ i 1)))
                  (d1 (aref ds j))
                  (d2 (aref ds (+ j 1))))
              (incf res (the fixnum (* (- c2 c1) (- d2 d1))))))))
      res)))

(declaim (inline intersect-p))
(defun intersect-p (l1 r1 l2 r2)
  (and (<= l1 r2) (<= l2 r1)))

(defun main ()
  (declare #.OPT)
  (let* ((n (read))
         (m (read))
         (abcs (make-array (+ n 2)))
         (defs (make-array (+ m 2)))
         (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)))
    (declare (uint16 n m))
    (dotimes (i n)
      (setf (aref abcs i) (list (read) (read) (read))))
    (setf (aref abcs n) (list 0 0 +neg-inf+)
          (aref abcs (+ n 1)) (list 0 0 +pos-inf+))
    (dotimes (i m)
      (setf (aref defs i) (list (read) (read) (read))))
    (setf (aref defs m) (list +neg-inf+ 0 0)
          (aref defs (+ m 1)) (list +pos-inf+ 0 0))
    (setq abcs (sort abcs (lambda (p1 p2)
                            (or (< (third p1) (third p2))
                                (and (= (third p1) (third p2))
                                     (< (second p1) (second p2)))))))
    (setq defs (sort defs (lambda (p1 p2)
                            (or (< (first p1) (first p2))
                                (and (= (first p1) (first p2))
                                     (< (third p1) (third p2)))))))
    (dotimes (i1 (+ n 2))
      (destructuring-bind (a1 b1 c1) (aref abcs i1)
        (declare (int32 a1 b1 c1))
        (loop for i2 from (+ i1 1) below (+ n 2)
              for (a2 b2 c2) of-type (int32 int32 int32) = (aref abcs i2)
              when (and (= c1 c2) (intersect-p a1 b1 a2 b2))
              do (minf a1 a2)
                 (maxf b1 b2))
        (setf (aref as i1) a1
              (aref bs i1) b1
              (aref cs i1) c1)))
    (dotimes (j1 (+ m 2))
      (destructuring-bind (d1 e1 f1) (aref defs j1)
        (declare (int32 d1 e1 f1))
        (loop for j2 from (+ j1 1) below (+ m 2)
              for (d2 e2 f2) of-type (int32 int32 int32) = (aref defs j2)
              when (and (= d1 d2) (intersect-p e1 f1 e2 f2))
              do (minf e1 e2)
                 (maxf f1 f2))
        (setf (aref ds j1) d1
              (aref es j1) e1
              (aref fs j1) f1)))
    (println (or (solve n m as bs cs ds es fs)
                 "INF"))))

#-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
")))