#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

fn main() {
    input! {
        n: usize,
        points: [(i64, i64, chars); n],
    }

    let points = points
        .into_iter()
        .map(|(x, y, chars)| (x * 2, y * 2, chars[0]))
        .collect::<Vec<_>>();

    let xf = |t: i64| {
        let mut maxv = -(1 << 60);
        let mut minv = 1 << 60;
        for &(x, _, c) in &points {
            let v = match c {
                'R' => x + t,
                'L' => x - t,
                _ => x,
            };
            maxv = max(v, maxv);
            minv = min(v, minv);
        }
        maxv - minv
    };

    let yf = |t: i64| {
        let mut maxv = -(1 << 60);
        let mut minv = 1 << 60;
        for &(_, y, c) in &points {
            let v = match c {
                'U' => y + t,
                'D' => y - t,
                _ => y,
            };
            maxv = max(v, maxv);
            minv = min(v, minv);
        }
        maxv - minv
    };

    let mut times = vec![0];

    let mut t = 0;
    loop {
        let delta = xf(t + 1) - xf(t);
        let mut ok = t;
        let mut ng = 1 << 60;
        for _ in 0..60 {
            let mid = (ok + ng) / 2;
            let d = xf(mid + 1) - xf(mid);
            if delta == d {
                ok = mid;
            } else {
                ng = mid;
            }
        }

        if ng != 1 << 60 && ok + 1 != t {
            times.push(ok + 1);
            t = ok + 1;
        } else {
            break;
        }
    }

    let mut t = 0;
    loop {
        let delta = yf(t + 1) - yf(t);
        let mut ok = t;
        let mut ng = 1 << 60;
        for _ in 0..60 {
            let mid = (ok + ng) / 2;
            let d = yf(mid + 1) - yf(mid);
            if d == delta {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        if ng != 1 << 60 as i64 && ok + 1 != t {
            times.push(ok + 1);
            t = ok + 1;
        } else {
            break;
        }
    }

    // println!("{:?}", times);

    let mut ans = 1 << 60;
    // println!("{}", ans);
    for &t in &times {
        let x = xf(t);
        let y = yf(t);
        let v = x * y;
        // println!("{}, {}, {}, {}, {}", t, x, y, v, v as f64 / 4.0);
        ans = min(v, ans);
    }
    println!("{}", ans as f64 / 4.0);
}


Measured memory_bytes: 12540