package main

import (
	"bufio"
	"fmt"
	"log"
	"os"
	"strconv"
)

// const abcd = "abcdefghijklmnopqrstuvwxyz"
// const ABCD = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

// var dy = [...]int{1, 1, 0, -1, -1, -1, 0, 1}
// var dx = [...]int{0, 1, 1, 1, 0, -1, -1, -1}

// var dx = [...]int{0, 1, 0, -1}
// var dy = [...]int{1, 0, -1, 0}

var inf int = 1e13
var mod = 1000000007

// ---------------------------------------------------------
func main() {
	log.SetFlags(log.Lshortfile)
	next := newScanner()
	N := next.Int()
	t := next.Ints(N)
	v := next.Ints(N)
	T := sum(t)
	ub := make([]int, T*2+1)
	for i := 0; i < T*2+1; i++ {
		ub[i] = inf
	}
	x := 0
	for i := 0; i < N; i++ {
		for y := 0; y < t[i]; y++ {
			ub[x] = min(ub[x], v[i]*2)
			ub[x+1] = min(ub[x+1], v[i]*2)
			ub[x+2] = min(ub[x+2], v[i]*2)
			x += 2
		}
	}
	ub[0] = 0
	ub[T*2] = 0
	for x := 0; x < T*2; x++ {
		ub[x+1] = min(ub[x+1], ub[x]+1)
	}
	for x := T * 2; x > 0; x-- {
		ub[x-1] = min(ub[x-1], ub[x]+1)
	}
	ans := 0.0
	for x := 0; x < T*2; x++ {
		ans += float64(ub[x]+ub[x+1]) / 2.0
	}
	fmt.Println(ans / 4)
}

// ---------------------------------------------------------

// Pair is liked C++ pair
type Pair struct {
	a, b int
}

// Pairs is sorted by []Pair struct
type Pairs []Pair

func (p Pairs) Len() int {
	return len(p)
}
func (p Pairs) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}

func (p Pairs) Less(i, j int) bool {
	if p[i].a < p[j].a {
		return true
	} else if p[i].a == p[j].a {
		return p[i].b < p[j].b
	}
	return false
}

// -------------------------------
func in(c, a, z int) bool {
	return c >= a && c < z
}

func btoi(b bool) int {
	if b {
		return 1
	}
	return 0
}

func itob(a int) bool {
	if a == 0 {
		return false
	}
	return true
}

func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}

func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}

func sum(a []int) int {
	r := 0
	for i := 0; i < len(a); i++ {
		r += a[i]
	}
	return r
}

func pro(a []int) int {
	r := 1
	for i := 0; i < len(a); i++ {
		r *= a[i]
	}
	return r
}

func fill(a []int, n int) []int {
	for i := 0; i < len(a); i++ {
		a[i] = n
	}
	return a
}

func minmax(a, b int) (int, int) {
	if a > b {
		return b, a
	}
	return a, b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// ---------- buffered scanner -----------------------------------------
type scanner struct {
	r   *bufio.Reader
	buf []byte
	p   int
}

func newScanner() *scanner {
	rdr := bufio.NewReaderSize(os.Stdin, 10000)
	return &scanner{r: rdr}
}
func (s *scanner) next() string {
	s.pre()
	start := s.p
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}
	result := string(s.buf[start:s.p])
	s.p++
	return result
}
func (s *scanner) Line() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)
	return string(s.buf[start:])
}
func (s *scanner) String() string {
	return s.next()
}
func (s *scanner) Int() int {
	v, _ := strconv.Atoi(s.next())
	return v
}
func (s *scanner) Ints(n int) []int {
	r := make([]int, n)
	for i := 0; i < n; i++ {
		r[i] = s.Int()
	}
	return r
}
func (s *scanner) Int64() int64 {
	v, _ := strconv.ParseInt(s.next(), 10, 64)
	return v
}
func (s *scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}
func (s *scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}


Measured memory_bytes: 896