Problem:
Score: 600 points

Problem Statement

There is a grass field that stretches infinitely.

In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).

There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).

What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.

Constraints

All values in input are integers between -10^9 and 10^9 (inclusive).

1 \leq N, M \leq 1000

A_i < B_i\ (1 \leq i \leq N)

E_j < F_j\ (1 \leq j \leq M)

The point (0, 0) does not lie on any of the given segments.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M

Output

If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \mathrm{cm^2}.

(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)

Sample Input 1

5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4

Sample Output 1

13

The area of the region the cow can reach is 13\ \mathrm{cm^2}.

Sample Input 2

6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4

Sample Output 2

INF

The area of the region the cow can reach is infinite.

Solution in Rust (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules !zero_one_impls {($({$Trait :ident $method :ident $($t :ty ) *,$e :expr } ) *) =>{$($(impl $Trait for $t {#[inline ] fn $method () ->Self {$e } } ) *) *} ;}
zero_one_impls !({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,0 } {Zero zero f32 f64 ,0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,1 } {One one f32 f64 ,1. } ) ;
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn new(s: &'a str) -> Self {
            let iter = s.split_ascii_whitespace();
            Self { iter }
        }
        #[inline]
        pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
            <T as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    macro_rules !iter_scan_impls {($($t :ty ) *) =>{$(impl IterScan for $t {type Output =Self ;#[inline ] fn scan <'a ,I :Iterator <Item =&'a str >>(iter :&mut I ) ->Option <Self >{iter .next () ?.parse ::<$t >() .ok () } } ) *} ;}
    iter_scan_impls !(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String ) ;
    macro_rules !iter_scan_tuple_impl {($($T :ident ) *) =>{impl <$($T :IterScan ) ,*>IterScan for ($($T ,) *) {type Output =($(<$T as IterScan >::Output ,) *) ;#[inline ] fn scan <'a ,It :Iterator <Item =&'a str >>(_iter :&mut It ) ->Option <Self ::Output >{Some (($(<$T as IterScan >::scan (_iter ) ?,) *) ) } } } ;}
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl !(A B ) ;
    iter_scan_tuple_impl !(A B C ) ;
    iter_scan_tuple_impl !(A B C D ) ;
    iter_scan_tuple_impl !(A B C D E ) ;
    iter_scan_tuple_impl !(A B C D E F ) ;
    iter_scan_tuple_impl !(A B C D E F G ) ;
    iter_scan_tuple_impl !(A B C D E F G H ) ;
    iter_scan_tuple_impl !(A B C D E F G H I ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J K ) ;
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(pub char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[macro_export]
macro_rules !min {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::min ($e ,min !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmin {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::min ($dst ,min !($($src ) ,+) ) ;$dst =x ;} } ;}
#[macro_export]
macro_rules !max {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::max ($e ,max !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmax {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::max ($dst ,max !($($src ) ,+) ) ;$dst =x ;} } ;}
fn main() {
    #![allow(unused_imports, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut _in_buf = Vec::new();
    stdin().read_to_end(&mut _in_buf).expect("io error");
    let _in_buf = unsafe { String::from_utf8_unchecked(_in_buf) };
    let mut scanner = Scanner::new(&_in_buf);
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :ty ;$len :expr ] ) =>{scanner .scan_vec ::<$t >($len ) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;([$t :ty ] ) =>{scanner .iter ::<$t >() } ;({$e :expr } ) =>{scanner .mscan ($e ) } ;($t :ty ) =>{scanner .scan ::<$t >() } ;}
    let _out = stdout();
    let mut _out = BufWriter::new(_out.lock());
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(_out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(_out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules! echo {
        ($iter :expr ) => {
            echo!($iter, '\n')
        };
        ($iter :expr ,$sep :expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!();
    let m = scan!();
    let abc = scan!([(i64, i64, i64); n]);
    let def = scan!([(i64, i64, i64); m]);
    let mut xs = vec![std::i64::MIN, 0, std::i64::MAX];
    let mut ys = vec![std::i64::MIN, 0, std::i64::MAX];
    xs.extend(abc.iter().map(|t| t.0));
    xs.extend(abc.iter().map(|t| t.1));
    ys.extend(abc.iter().map(|t| t.2));
    xs.extend(def.iter().map(|t| t.0));
    ys.extend(def.iter().map(|t| t.1));
    ys.extend(def.iter().map(|t| t.2));
    xs.sort();
    ys.sort();
    xs.dedup();
    ys.dedup();
    let h = xs.len();
    let w = ys.len();
    let mut ok = vec![vec![true; w * 2 + 1]; h * 2 + 1];
    let mut vis = vec![vec![false; w * 2 + 1]; h * 2 + 1];
    for (a, b, c) in abc.iter().cloned() {
        let aa = xs.binary_search(&a).unwrap();
        let bb = xs.binary_search(&b).unwrap();
        let cc = ys.binary_search(&c).unwrap();
        for x in aa * 2..=bb * 2 {
            ok[x][cc * 2] = false;
        }
    }
    for (d, e, f) in def.iter().cloned() {
        let dd = xs.binary_search(&d).unwrap();
        let ee = ys.binary_search(&e).unwrap();
        let ff = ys.binary_search(&f).unwrap();
        for y in ee * 2..=ff * 2 {
            ok[dd * 2][y] = false;
        }
    }
    let (s, t) = (
        xs.binary_search(&0).unwrap() * 2,
        ys.binary_search(&0).unwrap() * 2,
    );
    vis[s][t] = true;
    let mut st = vec![(s, t)];
    let g = GridGraph::new(h * 2 + 1, w * 2 + 1);
    while let Some((x, y)) = st.pop() {
        for (nx, ny) in g.adjacency4(x, y) {
            if nx == 0 || ny == 0 || nx == h * 2 || ny == w * 2 {
                println!("INF");
                return;
            }
            if ok[nx][ny] && !vis[nx][ny] {
                vis[nx][ny] = true;
                st.push((nx, ny));
            }
        }
    }
    let mut ans = 0;
    for i in (3..h * 2 - 3).step_by(2) {
        for j in (3..w * 2 - 3).step_by(2) {
            if vis[i][j] {
                ans += (xs[i / 2 + 1] - xs[i / 2]) * (ys[j / 2 + 1] - ys[j / 2]);
            }
        }
    }
    println!("{}", ans);
}
#[derive(Debug, Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct GridGraph {
    height: usize,
    width: usize,
}
impl GridGraph {
    pub fn new(height: usize, width: usize) -> Self {
        Self { height, width }
    }
    pub fn adjacency4(&self, x: usize, y: usize) -> Adjacent4<'_> {
        Adjacent4 {
            grid: self,
            x,
            y,
            state: 0,
        }
    }
    pub fn adjacency8(&self, x: usize, y: usize) -> Adjacent8<'_> {
        Adjacent8 {
            grid: self,
            x,
            y,
            state: 0,
        }
    }
}
#[derive(Debug)]
pub struct Adjacent4<'a> {
    grid: &'a GridGraph,
    x: usize,
    y: usize,
    state: usize,
}
impl<'a> Iterator for Adjacent4<'a> {
    type Item = (usize, usize);
    fn next(&mut self) -> Option<Self::Item> {
        const D: [(usize, usize); 4] = [(1, 0), (0, 1), (!0, 0), (0, !0)];
        for &(dx, dy) in D[self.state..].into_iter() {
            self.state += 1;
            let nx = self.x.wrapping_add(dx);
            let ny = self.y.wrapping_add(dy);
            if nx < self.grid.height && ny < self.grid.width {
                return Some((nx, ny));
            }
        }
        None
    }
}
#[derive(Debug)]
pub struct Adjacent8<'a> {
    grid: &'a GridGraph,
    x: usize,
    y: usize,
    state: usize,
}
impl<'a> Iterator for Adjacent8<'a> {
    type Item = (usize, usize);
    fn next(&mut self) -> Option<Self::Item> {
        const D: [(usize, usize); 8] = [
            (1, 0),
            (1, 1),
            (0, 1),
            (!0, 1),
            (!0, 0),
            (!0, !0),
            (0, !0),
            (1, !0),
        ];
        for &(dx, dy) in D[self.state..].into_iter() {
            self.state += 1;
            let nx = self.x.wrapping_add(dx);
            let ny = self.y.wrapping_add(dy);
            if nx < self.grid.height && ny < self.grid.width {
                return Some((nx, ny));
            }
        }
        None
    }
}