(in-package #:cl-user)

;;;
;;; Init
;;;

(eval-when (:compile-toplevel :load-toplevel :execute)
  ;; #+swank (declaim (optimize (speed 3) (safety 2)))
  #+swank (declaim (optimize (speed 0) (safety 3) (debug 3)))
  #-swank (declaim (optimize (speed 3) (safety 0) (debug 0)))
  #-swank (declaim (sb-ext:muffle-conditions sb-ext:compiler-note))
  #-swank (sb-ext:disable-debugger))

;;;
;;; Reader Macros
;;;

(eval-when (:compile-toplevel :load-toplevel :execute)
  (set-dispatch-macro-character
   #\# #\f
   #'(lambda (stream c2 n)
       (declare (ignore c2 n))
       (let ((form (read stream t nil t)))
         `(lambda (&optional %) (declare (ignorable %)) ,form))))

  (set-dispatch-macro-character
   #\# #\>
   #'(lambda (stream c2 n)
       (declare (ignore c2 n))
       (let ((form (read stream t nil t)))
         (declare (ignorable form))
         #-swank nil
         #+swank (if (atom form)
                     `(format *error-output* "~a => ~a~&" ',form ,form)
                     `(format *error-output* "~a => ~a~&" ',form `(,,@form)))))))

;;;
;;; Libraries
;;;

;;;
;;; BOF
;;;

(defpackage randomized-heap
  (:use #:cl)
  (:nicknames #:rh)
  (:shadow #:count)
  (:export #:make-randomized-heap
           #:empty-p
           #:push!
           #:pop!
           #:peak
           #:count
           #:do-all-kvs
           #:prune!))

(in-package #:randomized-heap)

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defvar *OPT*
    #+swank '(optimize (speed 3) (safety 2) (debug 3))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))))

(declaim (inline %make-node make-randomized-heap))
(defstruct (node (:constructor %make-node)
                 (:conc-name %n-))
  (key nil :type fixnum)
  (value nil :type t)
  (children (make-array 2 :element-type '(or null node)
                          :initial-element nil)
   :type (simple-array (or null node) (2))))

(defstruct (randomized-heap (:constructor make-randomized-heap (&optional (compare #'sb-impl::two-arg-<) (key-fn #'identity))))
  (root nil :type (or null node))
  (count 0 :type (integer 0 #.most-positive-fixnum))
  (comparator compare :type (function (fixnum fixnum) boolean))
  (key-fn key-fn :type (function (t) fixnum)))

(defun count (heap)
  (randomized-heap-count heap))

(declaim (inline %direction))
(defun %direction ()
  (declare #.*OPT*)
  (random 2))

(defun meld (l r comparator)
  (declare #.*OPT*
           ((or null node) l r)
           ((function (fixnum fixnum) boolean) comparator))
  (cond
    ((or (null l)
         (null r))
     (or l r))
    ((funcall comparator
              (%n-key l)
              (%n-key r))
     ;; l is root
     (let ((dir (%direction)))
       (setf (aref (%n-children l) dir)
             (meld (aref (%n-children l) dir)
                   r
                   comparator))
       l))
    (t
     ;; r is root
     (let ((dir (%direction)))
       (setf (aref (%n-children r) dir)
             (meld l
                   (aref (%n-children r) dir)
                   comparator))
       r))))

(declaim (inline peak))
(defun peak (heap)
  (declare #.*OPT*)
  (let ((root (randomized-heap-root heap)))
    (values (%n-value root)
            (%n-key root))))

(defun empty-p (heap)
  (null (randomized-heap-root heap)))

(declaim (inline pop! push!))
(defun pop! (heap)
  (declare #.*OPT*)
  (when (empty-p heap)
    (error "heap is empty"))
  (decf (randomized-heap-count heap))
  (multiple-value-bind (value key)
      (peak heap)
    (let* ((children (%n-children (randomized-heap-root heap)))
           (l (aref children 0))
           (r (aref children 1)))
      (setf (randomized-heap-root heap)
            (meld l
                  r
                  (randomized-heap-comparator heap)))
      (values value key))))

(defun push! (heap value)
  (declare #.*OPT*)
  (let ((key (funcall (randomized-heap-key-fn heap)
                      value)))
    (incf (randomized-heap-count heap))
    (setf (randomized-heap-root heap)
          (meld (randomized-heap-root heap)
                (%make-node :key key
                            :value value)
                (randomized-heap-comparator heap))))
  heap)

(defmacro do-all-kvs ((key value heap) &body body &environment env)
  (let ((temp (gensym)))
    (multiple-value-bind (args argvs res setter accessor)
        (get-setf-expansion heap env)
      `(let ((,temp (make-randomized-heap (randomized-heap-comparator ,accessor)
                                          (randomized-heap-key-fn ,accessor))))
         (loop :until (empty-p ,accessor)
               :do (multiple-value-bind (,value ,key)
                       (pop! ,accessor)
                     (progn ,@body)
                     (push! ,temp ,value)))
         (let* (,@(mapcar #'list args argvs)
                (,(car res) ,temp))
           ,setter
           nil)))))

(defun prune! (heap cnt)
  (let ((new-root nil)
        (comparator (randomized-heap-comparator heap)))
    (dotimes (_ cnt)
      (multiple-value-bind (v k) (pop! heap)
        (setf new-root
              (meld new-root
                    (%make-node :key k :value v)
                    comparator))))
    (setf (randomized-heap-root heap)
          new-root)))

;;;
;;; EOF
;;;

;;;
;;; Solution
;;;

(defpackage macro
  (:use #:cl)
  (:nicknames #:m)
  (:export #:while
           #:eval-always))

(in-package macro)

(defmacro while (test &body body)
  `(loop while ,test do (progn ,@body)))

(defmacro eval-always (&body body)
  `(eval-when (:compile-toplevel :load-toplevel :execute)
     ,@body))


(defpackage util
  (:use #:cl)
  (:nicknames #:u)
  (:export #:manhattan-dist
           #:+dir-dy-dx+
           #:+dy-dx+
           #:+dirs+
           #:coords->dir))

(in-package util)

(defun manhattan-dist (c1 c2)
  (+ (abs (- (car c1) (car c2)))
     (abs (- (cdr c1) (cdr c2)))))

(sb-int:defconstant-eqx +dir-dy-dx+
    '((#\U . (-1 . 0))
      (#\D . (1 . 0))
      (#\L . (0 . -1))
      (#\R . (0 . 1)))
  #'equalp)

(sb-int:defconstant-eqx +dy-dx+ (map 'list #'cdr +dir-dy-dx+) #'equal)
(sb-int:defconstant-eqx +dirs+ (map 'list #'car +dir-dy-dx+) #'equal)

(defun coords->dir (c1 c2)
  (destructuring-bind (y1 . x1) c1
    (destructuring-bind (y2 . x2) c2
      (let ((dy (signum (- y2 y1)))
            (dx (signum (- x2 x1))))
        (car (rassoc (cons dy dx) +dir-dy-dx+ :test #'equal))))))

#+swank
(progn
  (assert (eql #\R (coords->dir '(0 . 0) '(0 . 1))))
  (assert (eql #\D (coords->dir '(0 . 0) '(1 . 0))))
  (assert (eql #\U (coords->dir '(0 . 0) '(-1 . 0))))
  (assert (eql #\L (coords->dir '(0 . 0) '(0 . -1)))))


(in-package cl-user)

(defconstant +grid-size+ 60)
(defconstant +vital+ 1500)

(defstruct trap
  (id nil :type fixnum)
  (coord nil :type cons)
  (power nil :type fixnum)
  (interval nil :type fixnum))

;; jewel/start/goal/key をcheckpointと呼ぶことにする

(defstruct checkpoint
  (id nil :type fixnum)
  (coord nil :type cons)
  (type nil :type (member :jewel :start :goal :key)))

(defun get-trap-factor (grid traps)
  (let ((factors (make-array (list +grid-size+ +grid-size+) :element-type 'single-float
                                                            :initial-element 0.0)))
    (sb-int:dovector (trap traps)
      (destructuring-bind (sy . sx) (trap-coord trap)
        (loop for (dy . dx) in u:+dy-dx+
              do (loop with y = (+ sy dy)
                       with x = (+ sx dx)
                       while (and (<= 0 y (1- +grid-size+))
                                  (<= 0 x (1- +grid-size+))
                                  (not (find (aref grid y x)
                                             "#E")))
                       do (incf (aref factors y x) (/ (trap-power trap)
                                                      (trap-interval trap)))
                       do (incf y dy)
                          (incf x dx)))
        (incf (aref factors sy sx) (/ (trap-power trap)
                                      (trap-interval trap)))))
    factors))

(defun get-real-trap-factor (grid traps)
  (let ((factors (make-array (list +grid-size+ +grid-size+ 60) :element-type 'single-float
                                                               :initial-element 0.0)))
    (sb-int:dovector (trap traps)
      (destructuring-bind (sy . sx) (trap-coord trap)
        (loop for (dy . dx) in u:+dy-dx+
              do (loop with y = (+ sy dy)
                       with x = (+ sx dx)
                       while (and (<= 0 y (1- +grid-size+))
                                  (<= 0 x (1- +grid-size+))
                                  (not (find (aref grid y x)
                                             "#E")))
                       do (loop for dd below 60 by (trap-interval trap)
                                do (incf (aref factors y x dd) (/ (trap-power trap)
                                                                  (trap-interval trap))))
                       do (incf y dy)
                          (incf x dx)))
        (loop for dd below 60 by (trap-interval trap)
              do (incf (aref factors sy sx dd) (/ (trap-power trap)
                                                  (trap-interval trap))))))
    factors))

(defstruct (edge-between-checkpoints (:conc-name edge-))
  (dist-id nil :type fixnum)
  (estimated-cost nil :type single-float)
  (dirs nil :type list))

(defconstant +cost-threshold-between-checkpoints+ 100)

(defun get-estimated-cost-edges-between-checkpoints (grid checkpoints trap-factors)
  (let* ((n (length checkpoints))
         (coord-by-id (make-array n))
         (id-by-coord (make-hash-table :test #'equal))
         (edges-by-id (make-array n :initial-element nil)))
    (dolist (cp (coerce checkpoints 'list))
      (setf (gethash (checkpoint-coord cp) id-by-coord) (checkpoint-id cp)
            (aref coord-by-id (checkpoint-id cp)) (checkpoint-coord cp)))
    ;; 距離100以下でたどり着けるものと辺でつなぐ
    (sb-int:dovector (cp checkpoints)
      (destructuring-bind (sy . sx) (checkpoint-coord cp)
        (let (;; (cost y x path)
              (min-heap (rh:make-randomized-heap #'< #'first))
              (cost-by-coord (make-hash-table :test #'equal)))
          (rh:push! min-heap (list 0.0 sy sx nil))
          (m:while (not (rh:empty-p min-heap))
            (destructuring-bind (cost y x path) (rh:pop! min-heap)
              (when (<= cost #1=(gethash (cons y x) cost-by-coord (1+ +cost-threshold-between-checkpoints+)))
                (setf #1# cost)
                (let ((id (gethash (cons y x) id-by-coord)))
                  (when id
                    (push (make-edge-between-checkpoints :dist-id id
                                                         :estimated-cost cost
                                                         :dirs (reverse path))
                          (aref edges-by-id (checkpoint-id cp)))))
                (loop for (dy . dx) in u:+dy-dx+
                      for ny = (+ y dy)
                      for nx = (+ x dx)
                      when (and (<= 0 ny (1- +grid-size+))
                                (<= 0 nx (1- +grid-size+))
                                (not (find (aref grid ny nx)
                                           "#E"))
                                (< (+ cost
                                      (aref trap-factors ny nx)
                                      1)
                                   #2=(gethash (cons ny nx) cost-by-coord (1+ +cost-threshold-between-checkpoints+))))
                        do (setf #2# (+ cost (aref trap-factors ny nx) 1))
                        and do (rh:push! min-heap (list #2#
                                                        ny
                                                        nx
                                                        (cons (u:coords->dir (cons y x)
                                                                             (cons ny nx))
                                                              path))))))))))
    edges-by-id))

(defun get-estimated-costs-and-dirs-between-checkpoints (checkpoints edges-by-id)
  (let* ((n (length checkpoints))
         (costs-and-dirs (make-array (list n n) :initial-element (cons #.(expt 10 12) nil))))
    (dotimes (i n)
      (let (;; (cost id path)
            (min-heap (rh:make-randomized-heap #'< #'first)))
        (rh:push! min-heap (list 0.0 i nil))
        (m:while (not (rh:empty-p min-heap))
          (destructuring-bind (cost j path) (rh:pop! min-heap)
            (when (<= cost (car (aref costs-and-dirs i j)))
              (setf (aref costs-and-dirs i j)
                    (cons cost path))
              (dolist (edge (aref edges-by-id j))
                (let* ((k (edge-dist-id edge))
                       (nc (+ cost
                              (edge-estimated-cost edge)))
                       (npath (cons (edge-dirs edge) path)))
                  (when (< nc (car (aref costs-and-dirs i k)))
                    (setf (aref costs-and-dirs i k)
                          (cons nc npath))
                    (rh:push! min-heap (list nc k npath))))))))))
    (dotimes (i n)
      (dotimes (j n)
        (destructuring-bind (cost . dirs) (aref costs-and-dirs i j)
          (setf (aref costs-and-dirs i j)
                (cons cost (apply #'append (reverse dirs)))))))
    costs-and-dirs))


(defun find-chars (sm c)
  (destructuring-bind (h w) (array-dimensions sm)
    (let ((res nil))
      (dotimes (y h)
        (dotimes (x w)
          (when (eql (aref sm y x)
                     c)
            (push (cons y x)
                  res))))
      (reverse res))))

(defun orders->dirs (orders costs-and-dirs)
  (let ((res nil))
    (dotimes (i (1- (length orders)))
      (let* ((cp1 (aref orders i))
             (cp2 (aref orders (1+ i)))
             (dirs (cdr (aref costs-and-dirs (checkpoint-id cp1) (checkpoint-id cp2)))))
        (push dirs res)))
    (apply #'append (reverse res))))

(defun validate-dirs (grid dirs)
  (let* ((pos (first (find-chars grid #\S)))
         (key (first (find-chars grid #\K)))
         (y (car pos))
         (x (cdr pos))
         (key-visited nil))
    (dolist (dir dirs)
      (destructuring-bind (dy . dx) (cdr (assoc dir u:+dir-dy-dx+))
        (setf y (+ y dy))
        (setf x (+ x dx))
        (unless (and (<= 0 y (1- +grid-size+))
                     (<= 0 x (1- +grid-size+)))
          (error "out of grid"))
        (when (find (aref grid y x) "#E")
          (error "on trap or wall"))
        (when (equal (cons y x) key)
          (setf key-visited t))))
    (unless key-visited
      (error "key not unreached"))
    (unless (equal (cons y x)
                   (first (find-chars grid #\G)))
      (error "goal is ~a, but ended at ~a" (first (find-chars grid #\G)) (cons y x)))))

(defun get-insts (grid dirs traps)
  "ゴールできない場合はnilを返す"
  (let* ((pos (first (find-chars grid #\S)))
         (key (first (find-chars grid #\K)))
         (y (car pos))
         (x (cdr pos))
         (factors (get-real-trap-factor grid traps))
         (res nil)
         (rest-vital +vital+)
         (key-visited nil)
         (turn 0))
    (dolist (dir dirs)
      (destructuring-bind (dy . dx) (cdr (assoc dir u:+dir-dy-dx+))
        (setf y (+ y dy))
        (setf x (+ x dx))
        (push (cons :move dir) res)
        (unless (and (<= 0 y (1- +grid-size+))
                     (<= 0 x (1- +grid-size+)))
          (error "out of grid"))
        (when (find (aref grid y x) "#E")
          (error "on trap or wall"))
        (when (equal (cons y x) key)
          (setf key-visited t))
        (decf rest-vital (aref factors y x (rem turn 60)))
        (when (minusp rest-vital)
          (return-from get-insts nil))
        (incf turn)))
    #>rest-vital
    (unless key-visited
      (error "key not unreached"))
    (unless (equal (cons y x)
                   (first (find-chars grid #\G)))
      (error "goal is ~a, but ended at ~a" (first (find-chars grid #\G)) (cons y x)))
    (reverse res)))

(defun main ()
  (let* ((n (read))
         (d (read))
         (h (read))
         (grid (make-array (list n n) :element-type 'base-char
                                      :initial-element #\Nul))
         (checkpoints (make-array 0 :fill-pointer 0))
         (traps (make-array 0 :fill-pointer 0)))
    (dotimes (y n)
      (let ((tmp (read-line)))
        (dotimes (x n)
          (setf (aref grid y x) (char tmp x))
          (ecase (char tmp x)
            ((#\S #\K #\G #\J)
             (vector-push-extend (make-checkpoint :id (fill-pointer checkpoints)
                                                  :coord (cons y x)
                                                  :type (ecase (char tmp x)
                                                          (#\S :start)
                                                          (#\K :key)
                                                          (#\G :goal)
                                                          (#\J :jewel)))
                                 checkpoints))
            ;; 残りは一旦無視
            ((#\T #\E #\. #\F #\#)
             nil)))))
    #> checkpoints
    (dotimes (_ (read))
      (vector-push-extend
       (make-trap :id (fill-pointer traps)
                  :coord (cons (read) (read))
                  :power d
                  :interval (read))
       traps))
    (let* ((trap-factors (get-trap-factor grid traps))
           (edges-by-cp-id (get-estimated-cost-edges-between-checkpoints grid checkpoints trap-factors))
           (costs-and-dirs (get-estimated-costs-and-dirs-between-checkpoints checkpoints edges-by-cp-id))
           (find-checkpoint (lambda (type)
                              (find-if (lambda (cp)
                                         (eq (checkpoint-type cp) type))
                                       checkpoints)))
           (start (funcall find-checkpoint :start))
           (goal (funcall find-checkpoint :goal))
           (key (funcall find-checkpoint :key))
           (fixed (list start key goal)))
      ;; #>costs-and-dirs
      (loop for est-vital downfrom (- h 100) to (- h 500) by 100 do
        (let* ((orders (vector start key goal))
               (cost (loop for i below (1- (length orders))
                           for cp1 = (aref orders i)
                           for cp2 = (aref orders (1+ i))
                           sum (car (aref costs-and-dirs
                                          (checkpoint-id cp1)
                                          (checkpoint-id cp2))))))
          #>cost
          (sb-int:dovector (cp checkpoints)
            (unless (find cp fixed :test #'eq)
              (let ((orders-len (length orders))
                    (insert-index -1)
                    (min-cost-diff #.(expt 10 12)))
                (loop for i from 1 below (1- orders-len)
                      for c1 = (car (aref costs-and-dirs
                                          (checkpoint-id (aref orders (1- i)))
                                          (checkpoint-id cp)))
                      for c2 = (car (aref costs-and-dirs
                                          (checkpoint-id cp)
                                          (checkpoint-id (aref orders i))))
                      for c3 = (car (aref costs-and-dirs
                                          (checkpoint-id (aref orders (1- i)))
                                          (checkpoint-id (aref orders i))))
                      for cost-diff = (+ c1 c2 (- c3))
                      when (< cost-diff min-cost-diff)
                        do (setf min-cost-diff cost-diff
                                 insert-index i))
                (when (and (>= insert-index 1)
                           (<= (+ cost min-cost-diff) est-vital))
                  (setf orders (concatenate 'vector
                                            (subseq orders 0 insert-index)
                                            (vector cp)
                                            (subseq orders insert-index)))
                  (incf cost min-cost-diff)))))
          #>orders
          (let* ((dirs (orders->dirs orders costs-and-dirs))
                 (insts (get-insts grid dirs traps)))
            (when insts
              #>est-vital
              (dolist (inst insts)
                (ecase (car inst)
                  (:move
                   (format t "M ~a~%" (cdr inst)))))
              (return))))))))

#-swank (main)

;;;
;;; Debug
;;;

#+swank
(defun run ()
  (let ((*standard-input*
          (make-string-input-stream
           (with-output-to-string (*standard-output*)
             (run-program
              (truename "~/.roswell/bin/copy-or-paste")
              '()
              :output *standard-output*)))))
    (main)))

;; Raise error on warning at compile time

#+(and sbcl (not swank))
(eval-when (:compile-toplevel)
  (when (or (plusp sb-c::*compiler-warning-count*)
            sb-c::*undefined-warnings*)
    (error "compiler-error-count:~a, undefined warnings:~a"
           sb-c::*compiler-warning-count*
           sb-c::*undefined-warnings*)))

#+swank
(defun run-sample (infile outfile &optional (out *standard-output*))
  (with-open-file (*standard-input* infile :direction :input)
    (with-open-file (*standard-output* outfile :direction :output
                                               :if-exists :supersede)
      (main))
    (sb-ext:run-program "/usr/bin/java" (list "Judge" infile outfile)
                        :output out
                        :error *error-output*)))

#+swank (declaim (notinline run-sample-zero))
#+swank
(defun run-sample-zero ()
  (gc :full t)
  (with-input-from-string (*standard-input* "60 3 1500
.......JJ....J#..#E#....EE.J..E...E#J.....#.#EE......#..J.J#
#E#.....##J..JE....E..#....J.........#......#..#J.........#.
.J.J.#.#....J.#..#........J#...#J#.KJE.J.E.#J.#....#......J.
J..E..#.E#.......E........JEJ.....F..##..............#...J.J
..J.......JE...#......J.#.#..#J#JFJ.......E..#..#....E.....J
#..J.....EE....J........E............##.E#.E.#JJ..........E.
...#......J.J..J#...#...#.#..JE#....##E...#F.#....E....#E#..
.JJ.....###.J.EE...J...#E#E#...E.E.....#E......J..#...#....#
E.E.......#JF.J.J.E.##E#...EE..J....F..#.#J#..E#J..E..J...#F
##....F.#F#.E.#.EJ...J#E..#..#.J.......E...J....#..#..#....S
.E...E...J..J#........#...E.E.......#.....J..J.....E..E....#
.................#J#.....F...JE.#......##.........JJ.J....#.
E..J...E##..#.J...#...#.E....##...#.....EEJJJ.##.#.E.....E#.
E#.F.#.......JF..#..E#......EJ.....#.#.E.##..JJ.......E.J..E
JE..#E....E..E.J#.E...E...J...#J#J.#.E.....E..#E#.E..EF###..
E....J.#..J#....#..EE#.E...E.J.J...E#E#.J..J...E..........J#
.....#..J.#JF.#....E..#EE..E..#.......E.........#..J..#..J.F
#.EF.......E.J.E............#.........#...........E...#.#J..
F.....JJ...E#..E.#....#.E#...#...F.J.#.E.F.#.....J.....#EJ.E
###......#.E.J.E...#E..#..E...#.....#..#.#......F#.E.J..#.#E
....JEEE..EE.#.E#..#JJ............#J.E.#E..J........E....#.E
..E....EJ...J........#..J..J.#E#.#...#.E....#E.#E.#.#E..#..#
...#E#.E.....#J.E.#.#.J.J...E.JJ#J...#.J...##....J.J.......#
.....F....#..J#J..#....#.E...EJ#..#...#.#F#F.EE#..#.....#E.E
J#..#....#.#E..#.J.#.#......EJ..J.............#...#....#.E..
..##EEEE.....JJ..J.#..#..#.E....#J#E#E...E......#JJ#.E..E.#J
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")
    (main)))