(use util.queue)(use util.match)(use gauche.collection)(use gauche.sequence)
(define-syntax def-syntax (syntax-rules()((_ v e ...)(define-syntax v (syntax-rules e ...)))))
(define-syntax def-const define-constant)(define-syntax def define)(define-syntax def-inline define-inline)
(def-syntax def-names ()((_[x y]...)(begin(define-constant x y)...)))
(def-names [// quotient][% modulo][v-make make-vector][v-ref vector-ref][v-set! vector-set!][ht-make make-hash-table][ht-ref hash-table-get][ht-set! hash-table-put!][ht-keys hash-table-keys][ht-values hash-table-values][q-make make-queue][make-q make-queue][enq! enqueue!][deq! dequeue!][q-empty? queue-empty?])
(def-syntax input (: list vec cons str)
  ((_ : cons e ...)(cons(input : e ...)(input : e ...)))((_ : list str)(input : string->list str))
  ((_ : vec str)(input : string->vector str))((_ : vec n e ...)(vector-tabulate n(^_(input : e ...))))
  ((_ : list n e ...)(let l([k n])(if(zero? k)'()(cons(input : e ...)(l(- k 1))))))((_ :)(read))((_ : : e)e)
  ((_ : str)(let1 s(read-line)(if(string=? s "")(read-line)s)))((_[[v]: e ...])(def v(input : e ...)))
  ((_[[v w ...]: e ...])(begin(def v(input : e ...))(input[[w ...]: e ...])))
  ((_[v : e ...])(def v(input : e ...)))((_ : op e ...)(op(input : e ...)))
  ((_(e ...))(e ...))((_ v)(def v(read)))((_ e ...)(begin(input e)...)))

(define-constant *MOD* 1000000007)
;(define-constant *MOD* 998244353)
(def-syntax add-mod! ()((_ v x)(let1 y(+ v x)(set! v(if(< y *MOD*)y(- y *MOD*))))))
(def-inline(v-add-mod! v i x)(let1 y(+(v-ref v i)x)(v-set! v i(if(< y *MOD*)y(- y *MOD*)))))
(def-syntax max! ()((_ v x)(set! v (max x v)))) (def-syntax min! ()((_ v x)(set! v (min x v))))
(def-inline(v-add! v i x)(v-set! v i(+ x(v-ref v i))))
(def-inline(ht-add! ht i x)(ht-set! ht i(+ x(ht-ref ht i 0))))
(def-inline(ht-cons! ht i x)(ht-set! ht i(cons x(ht-ref ht i '()))))
(def-syntax return () ((_ e ...) (begin (print e ...) (exit))))

;; 以下スニペットのコピペ


;; 以下が本体

(input N [[A B] : vec N])
(def asum (make-vector N 0))
(def bsum (make-vector N 0))
(let loop[[i (- N 1)] [a (v-ref A (- N 1))] [b (v-ref B (- N 1))]]
  (v-set! asum i a)
  (v-set! bsum i b)
  (unless (zero? i)
    (loop (- i 1) (+ a (v-ref A (- i 1))) (+ b (v-ref B (- i 1))))))

(def (culc-x A B)
  (sqrt (/ (exact->inexact A) B)))
(def (culc-t x A B)
  (+ (/ A x) (* B x)))

(def ans 0.0)
(def x 1.0)
(dotimes [i N]
  (set! x (max x (min (culc-x (v-ref A i) (v-ref B i))
                      (culc-x (v-ref asum i) (v-ref bsum i)))))
  (inc! ans (culc-t x (v-ref A i) (v-ref B i))))
(print ans)