#![allow(unused_imports, unused_macros, unknown_lints)]

use std::collections::*;
use std::f64::*;
use std::cmp::*;
use std::cmp::Ordering::*;

macro_rules! dump {($($e:expr), +) => {println!(concat!($(stringify!($e), " = {:?}\n"), +), $($e), +)}}
macro_rules! max {($e0:expr, $($e:expr), +) => {{let mut r = $e0; $(r = max(r, $e);)+ r}}}
macro_rules! min {($e0:expr, $($e:expr), +) => {{let mut r = $e0; $(r = min(r, $e);)+ r}}}
macro_rules! freq {($v:expr) => {{let mut h = HashMap::new(); for x in $v {*h.entry(x).or_insert(0) += 1} h}}}

fn main() {
  let n = get::val::<usize>();
  let ts = get::vec::<usize>();
  let vs = get::vec::<usize>();

  let t_end = ts.iter().sum::<usize>();

  let lrs = {
    let mut buf = vec![];
    let mut acc = 0;
    buf.push((0,0));
    for t in ts {
      buf.push((acc,acc+t));
      acc += t
    }
    buf.push((acc,acc));
    buf
  };
  
  let mut ans = 0.0;
  let mut prev = 0.0;
  for t in (0..2*t_end+1).map(|x|x as f64 / 2.0) {
    let f = |(i,&(l,r))| {
      let v = if i==0 || i==n+1 {0.0} else {vs[i-1] as f64};
      let l = l as f64;
      let r = r as f64;
      if t<l {v+(l-t)} else if t<=r {v} else {v+(t-r)}
    };
    let vmax = lrs.iter().enumerate().map(f).fold(std::f64::INFINITY,|a,x|f64::min(a,x));
    ans += (prev + vmax) * 0.25;
    prev = vmax
  }

  println!("{}", ans)
}

#[allow(dead_code)]
mod get {
  use std::io::*;
  use std::str::*;
  use std::process::*;

  pub fn val<T: FromStr>() -> T {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    buf.trim_right().parse::<T>().ok().unwrap()
  }

  pub fn vals<T: FromStr>(n: usize) -> Vec<T> {
    let mut vec: Vec<T> = vec![];
    for _ in 0 .. n {
      vec.push(val());
    }
    vec
  }

  pub fn tuple<T1: FromStr, T2: FromStr>() -> (T1, T2) {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    let mut it = buf.trim_right().split_whitespace();
    let x = it.next().unwrap().parse::<T1>().ok().unwrap();
    let y = it.next().unwrap().parse::<T2>().ok().unwrap();
    (x, y)
  }

  pub fn tuples<T1: FromStr, T2: FromStr>(n: usize) -> Vec<(T1, T2)> {
    let mut vec: Vec<(T1, T2)> = vec![];
    for _ in 0 .. n {
      vec.push(tuple());
    }
    vec
  }

  pub fn tuple3<T1: FromStr, T2: FromStr, T3: FromStr>() -> (T1, T2, T3) {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    let mut it = buf.trim_right().split_whitespace();
    let x = it.next().unwrap().parse::<T1>().ok().unwrap();
    let y = it.next().unwrap().parse::<T2>().ok().unwrap();
    let z = it.next().unwrap().parse::<T3>().ok().unwrap();
    (x, y, z)
  }

  pub fn tuple3s<T1: FromStr, T2: FromStr, T3: FromStr>(n: usize) -> Vec<(T1, T2, T3)> {
    let mut vec: Vec<(T1, T2, T3)> = vec![];
    for _ in 0 .. n {
      vec.push(tuple3());
    }
    vec
  }

  pub fn vec<T: FromStr>() -> Vec<T> {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    buf.trim_right().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
  }

  pub fn mat<T: FromStr>(h: usize) -> Vec<Vec<T>> {
    let mut mat = vec![];
    for _ in 0 .. h {
      mat.push(vec());
    }
    mat
  }

  pub fn chars() -> Vec<char> {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    buf.trim_right().chars().collect()
  }
}

#[allow(dead_code)]
mod put {
  use std::string::*;

  pub fn vec<T: ToString>(vec: &Vec<T>, sep: &str) {
    let out = vec.iter().map(|e| e.to_string()).collect::<Vec<_>>().as_slice().join(sep);
    println!("{}", out);
  }

  pub fn mat<T: ToString>(mat: &Vec<Vec<T>>, sep: &str) {
    for v in mat {
      vec(v, sep);
    }
  }
}



Measured memory_bytes: 4352