Problem:
Score : 300 points

Problem Statement

Dolphin resides in two-dimensional Cartesian plane, with the positive x-axis pointing right and the positive y-axis pointing up.

Currently, he is located at the point (sx,sy). In each second, he can move up, down, left or right by a distance of 1.

Here, both the x- and y-coordinates before and after each movement must be integers.

He will first visit the point (tx,ty) where sx < tx and sy < ty, then go back to the point (sx,sy), then visit the point (tx,ty) again, and lastly go back to the point (sx,sy).

Here, during the whole travel, he is not allowed to pass through the same point more than once, except the points (sx,sy) and (tx,ty).

Under this condition, find a shortest path for him.

Constraints

-1000 ≤ sx < tx ≤ 1000

-1000 ≤ sy < ty ≤ 1000

sx,sy,tx and ty are integers.

Input

The input is given from Standard Input in the following format:

sx sy tx ty

Output

Print a string S that represents a shortest path for Dolphin.

The i-th character in S should correspond to his i-th movement.

The directions of the movements should be indicated by the following characters:

U: Up

D: Down

L: Left

R: Right

If there exist multiple shortest paths under the condition, print any of them.

Sample Input 1

0 0 1 2

Sample Output 1

UURDDLLUUURRDRDDDLLU

One possible shortest path is:

Going from (sx,sy) to (tx,ty) for the first time: (0,0) → (0,1) → (0,2) → (1,2)

Going from (tx,ty) to (sx,sy) for the first time: (1,2) → (1,1) → (1,0) → (0,0)

Going from (sx,sy) to (tx,ty) for the second time: (0,0) → (-1,0) → (-1,1) → (-1,2) → (-1,3) → (0,3) → (1,3) → (1,2)

Going from (tx,ty) to (sx,sy) for the second time: (1,2) → (2,2) → (2,1) → (2,0) → (2,-1) → (1,-1) → (0,-1) → (0,0)

Sample Input 2

-2 -2 1 1

Sample Output 2

UURRURRDDDLLDLLULUUURRURRDDDLLDL

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

#|
------------------------------------
|               Utils               |
------------------------------------
|#


(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print :fiveam))
                 (shadow :run)
                 (use-package :fiveam)))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

#-swank
(unless (member :child-sbcl *features*)
  (quit
   :unix-status
   (process-exit-code
    (run-program *runtime-pathname*
                 `("--control-stack-size" "128MB"
                   "--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
                   "--eval" "(push :child-sbcl *features*)"
                   "--script" ,(namestring *load-pathname*))
                 :output t :error t :input t))))


(defconstant +mod+ 1000000007)


(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~a" b)) () '(signed-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~a" b)) () '(unsigned-byte ,b))) bits)))

(define-int-types 2 4 8 16 32 64)


(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1
        (write obj :stream stream)
      (fresh-line stream))))

(defmacro safe-sort (list test &key (key #'identity))
  `(progn
    (declaim (inline sort sb-impl::stable-sort-list))
    (sort (copy-seq ,list) ,test :key ,key)))

(defmacro read-numbers-to-list (size)
  `(loop repeat ,size collect (read)))

(defmacro read-numbers-to-array (size)
  (let ((i (gensym))
        (arr (gensym)))
    `(let ((,arr (make-array ,size
                             :element-type 'fixnum)))
       (declare ((array fixnum 1) ,arr))
       (loop for ,i of-type fixnum below ,size do
            (setf (aref ,arr ,i) (read))
          finally
            (return ,arr)))))

(defmacro read-characters-to-board (row-size column-size)
  (let ((board (gensym))
        (r (gensym))
        (c (gensym))
        (tmp (gensym)))
    `(let ((,board (make-array '(,row-size ,column-size) :element-type 'character :adjustable nil)))
       (dotimes (,r ,row-size ,board)
         (let ((,tmp (read-line)))
           (dotimes (,c ,column-size)
             (setf (aref ,board ,r ,c) (char ,tmp ,c))))))))

(defmethod princ-for-each-line ((sequence list))
  (format t "~{~a~&~}" sequence))

(defmethod princ-for-each-line ((sequence vector))
  (loop for i below (length sequence) do
       (princ (aref sequence i))
       (fresh-line)))

(declaim (inline unwrap))
(defun unwrap (list)
  (the string
       (format nil "~{~a~^ ~}" list)))

(defmacro with-buffered-stdout (&body body)
  (let ((out (gensym)))
    `(let ((,out (make-string-output-stream :element-type 'base-char)))
       (let ((*standard-output* ,out))
         ,@body)
       (write-string (get-output-stream-string ,out)))))

(defmacro maxf (place cand)
  `(setf ,place (max ,place ,cand)))

(defmacro minf (place cand)
  `(setf ,place (min ,place ,cand)))


(defmacro alambda (parms &body body)
  `(labels ((self ,parms ,@body))
     #'self))

(defun iota (count &optional (start 0) (step 1))
  (loop for i from 0 below count collect (+ start (* i step))))


#|
------------------------------------
|               Body               |
------------------------------------
|#


(defun solve (sx sy gx gy)
  (let ((dx (- gx sx))
        (dy (- gy sy)))
    (concatenate 'string
                 (loop repeat dx collect #\R)
                 (loop repeat dy collect #\U)
                 (loop repeat dy collect #\L)
                 (loop repeat dy collect #\D)
                 '(#\D)
                 (loop repeat (+ dx 1) collect #\R)
                 (loop repeat (+ dy 1) collect #\U)
                 '(#\L)
                 '(#\U)
                 (loop repeat (+ dx 1) collect #\L)
                 (loop repeat (+ dy 1) collect #\D)
                 '(#\R))))



(defun main ()
  (declare #.OPT)
  (destructuring-bind (sx sy gx gy) (loop repeat 4 collect (read))
    (princ (solve sx sy gx gy))
    (fresh-line)))

#-swank (main)