;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (ql:quickload '(:cl-debug-print :fiveam))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
;; unfinished.

(declaim (inline find-argopt))
(defun find-argopt (sequence predicate &key (start 0) end (key #'identity))
  "Returns an index x that satisfies (NOT (FUNCALL PREDICATE SEQUENCE[y]
SEQUENCE[x])) (i.e. SEQUENCE[x] >= SEQUENCE[y]) for all the indices y and
returns SEQUENCE[x] as the second value."
  (declare ((or null (integer 0 #.most-positive-fixnum)) end)
           ((integer 0 #.most-positive-fixnum) start)
           (function predicate)
           (sequence sequence))
  (etypecase sequence
    (list
     (let ((end (or end most-positive-fixnum))
           (optimum (funcall key (car sequence)))
           (index 0)
           (pos 0))
       (dolist (x sequence (values index optimum))
         (when (>= pos end)
           (return (values index optimum)))
         (when (>= pos start)
           (unless (funcall predicate optimum (funcall key x))
             (setq optimum (funcall key x)
                   index pos)))
         (incf pos))))
    (vector
     (let ((end (or end (length sequence))))
       (unless (<= start end)
         (error "Can't find optimal value in null interval [~A, ~A)" start end))
       (let ((optimum (funcall key (aref sequence 0)))
             (index 0))
         (dotimes (i (length sequence) (values index optimum))
           (unless (funcall predicate optimum (funcall key (aref sequence i)))
             (setq optimum (aref sequence i)
                   index i))))))))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  (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 #\-))
                                  (setf 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))))))))

(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 +eps+ 1d-10)

(defun main ()
  (let* ((init-x (float (read) 1d0))
         (init-y (float (read) 1d0))
         (goal-x (float (read) 1d0))
         (goal-y (float (read) 1d0))
         (n (read))
         (xs (make-array (+ n 2) :element-type 'double-float))
         (ys (make-array (+ n 2) :element-type 'double-float))
         (rs (make-array (+ n 2) :element-type 'double-float :initial-element 0d0))
         (init n)
         (goal (+ 1 n))
         (q (loop for i below (+ n 2) collect i))
         (dists (make-array (+ n 2) :element-type 'double-float :initial-element most-positive-double-float)))
    (declare ((simple-array double-float (*)) dists)
             (list q)
             (uint16 n))
    (dotimes (i n)
      (setf (aref xs i) (float (read-fixnum) 1d0)
            (aref ys i) (float (read-fixnum) 1d0)
            (aref rs i) (float (read-fixnum) 1d0)))
    (setf (aref xs init) init-x
          (aref ys init) init-y
          (aref xs goal) goal-x
          (aref ys goal) goal-y
          (aref dists init) 0d0)
    (loop until (null q)
          for i = (find-argopt q #'< :key (lambda (v) (aref dists v)))
          for v = (nth i q)
          for x0 = (aref xs v)
          for y0 = (aref ys v)
          for r0 = (aref rs v)
          do (setf q (delete v q :count 1))
             (dotimes (next (+ n 2))
               (let* ((x1 (aref xs next))
                      (y1 (aref ys next))
                      (r1 (aref rs next))
                      (delta (max 0d0 (- (sqrt (+ (expt (- x0 x1) 2)
                                                  (expt (- y0 y1) 2)))
                                         r0 r1))))
                 (when (< (+ (aref dists v) delta +eps+)
                          (aref dists next))
                   (setf (aref dists next)
                         (+ (aref dists v) delta))))))
    (println (aref dists goal))))

#-swank (main)


Measured memory_bytes: 17252