//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

use input::*;

fn get_limit(p: f64, t: &Vec<f64>, v: &Vec<f64>) -> f64 {
    let mut res = 999999999.0;

    let mut offset = 0.0;
    for i in 0..t.len() {
        let buf = (offset - p).abs() + v[i];
        if res > buf {
            res = buf;
        }
        let buf = (offset - p + t[i]).abs() + v[i];
        if res > buf {
            res = buf;
        }
        if offset <= p && p <= offset + t[i] {
            let buf = v[i];
            if res > buf {
                res = buf;
            }
        }
        offset += t[i];
    }

    res
}

fn main() {
    let n: usize;
    input!(n);

    let mut t = input_vector::<f64>();
    let mut v = input_vector::<f64>();
    t.push(0.0);
    v.push(0.0);
    t.insert(0, 0.0);
    v.insert(0, 0.0);

    let sum_t = t.iter().sum::<f64>();

    let mut time = 0.0;
    let mut ans = 0.0;

    while time < sum_t {
        let l1 = get_limit(time, &t, &v);
        let l2 = get_limit(time + 0.5, &t, &v);
        //println!("{} {}", time, l1);
        ans += (l1 * 0.5 + l2 * 0.5) / 2.0;

        time += 0.5;
    }
    println!("{}", ans);
}


Measured memory_bytes: 4352