#-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))))
(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))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setq minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
        (let* ((byte (%read-byte)))
          (if (<= 48 byte 57)
              (setq result (+ (- byte 48)
                              (* 10 (the (integer 0 #.(floor most-positive-fixnum 10))
                                         result))))
              (return (if minus (- result) result))))))))

;;;
;;; Diameter of tree
;;;

(declaim (inline find-diameter))
(defun find-diameter (graph)
  "Finds a diameter of a tree."
  (declare (vector graph))
  (assert (> (length graph) 0))
  (let ((end 0)
        (max-depth 0)
        res)
    (labels ((dfs (v parent depth)
               (declare ((integer 0 #.array-total-size-limit) v parent depth))
               (when (> depth max-depth)
                 (setq max-depth depth
                       end v))
               (dolist (child (aref graph v))
                 (declare ((mod #.most-positive-fixnum) child))
                 (unless (= child parent)
                   (dfs child v (+ depth 1))))))
      (dfs 0 array-total-size-limit 0)
      (setq max-depth 0)
      (labels ((dfs2 (v parent depth path)
                 (declare ((integer 0 #.array-total-size-limit) v parent))
                 (when (> depth max-depth)
                   (setq max-depth depth
                         res path))
                 (dolist (child (aref graph v))
                   (declare ((mod #.array-total-size-limit) child))
                   (unless (= child parent)
                     (dfs2 child v (+ depth 1) (cons child path))))))
        (dfs2 end array-total-size-limit 0 (list end))
        res))))

(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
;;;

(defun solve1 (graph center)
  (let* ((n (length graph))
         (dp (make-array (+ n 1) :element-type 'uint31 :initial-element 1)))
    (labels ((get-depth (v parent)
               (let ((max-depth 0))
                 (dolist (child (aref graph v))
                   (unless (= child parent)
                     (maxf max-depth (+ 1 (get-depth child v)))))
                 max-depth))
             (dfs (v parent depth)
               (let ((res 0))
                   (dolist (child (aref graph v))
                     (unless (= child parent)
                       (incf res)
                       (dfs child v (+ depth 1))))
                   (maxf (aref dp depth) res))))
      (let ((res1 (loop for child in (aref graph center)
                        maximize (+ 2 (get-depth child center)))))
        (dfs center -1 0)
        (values res1 (reduce #'* dp))))))

(defun solve2 (graph center1 center2)
  (let* ((n (length graph))
         (dp (make-array (+ n 1) :element-type 'uint31 :initial-element 1)))
    (setf (aref dp 0) 2)
    (labels ((get-depth (v parent)
               (let ((max-depth 0))
                 (dolist (child (aref graph v))
                   (unless (= child parent)
                     (maxf max-depth (+ 1 (get-depth child v)))))
                 max-depth))
             (dfs (v parent depth)
               (let ((res 0))
                   (dolist (child (aref graph v))
                     (unless (= child parent)
                       (incf res)
                       (dfs child v (+ depth 1))))
                   (maxf (aref dp depth) res))))
      (let ((res1 (+ 1 (max (get-depth center1 center2)
                            (get-depth center2 center1)))))
        (dfs center1 center2 1)
        (dfs center2 center1 1)
        (values res1 (reduce #'* dp))))))

(defun main ()
  (let* ((n (read))
         (as (make-array n :element-type 'uint31 :initial-element 0))
         (bs (make-array n :element-type 'uint31 :initial-element 0))
         (graph (make-array n :element-type 'list :initial-element nil)))
    (dotimes (i (- n 1))
      (let ((a (- (read-fixnum) 1))
            (b (- (read-fixnum) 1)))
        (setf (aref as i) a
              (aref bs i) b)
        (push a (aref graph b))
        (push b (aref graph a))))
    (let ((min1 #.(expt 2 64))
          (min2 #.(expt 2 64)))
      (dotimes (i n)
        (multiple-value-bind (res1 res2) (solve1 graph i)
          (when (or (< res1 min1)
                    (and (= res1 min1)
                         (< res2 min2)))
            (setq min1 res1 min2 res2))))
      (loop for a across as
            for b across bs
            do (multiple-value-bind (res1 res2) (solve2 graph a b)
                 (when (or (< res1 min1)
                           (and (= res1 min1)
                                (< res2 min2)))
                   (setq min1 res1 min2 res2))))
      (format t "~D ~D~%" min1 min2))))

#-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
1 2
2 3
3 4
3 5
"
    "2 4
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "8
1 2
2 3
4 3
5 4
6 7
6 8
3 6
"
    "3 4
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10
1 2
2 3
3 4
4 5
5 6
6 7
3 8
5 9
3 10
"
    "4 6
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "13
5 6
6 4
2 8
4 7
8 9
3 2
10 4
11 10
2 4
13 10
1 8
12 1
"
    "4 12
")))


Measured memory_bytes: 42300