Problem:
Score : 400 points

Problem Statement

On a two-dimensional plane, there are N red points and N blue points.
The coordinates of the i-th red point are (a_i, b_i), and the coordinates of the i-th blue point are (c_i, d_i).

A red point and a blue point can form a friendly pair when, the x-coordinate of the red point is smaller than that of the blue point, and the y-coordinate of the red point is also smaller than that of the blue point.

At most how many friendly pairs can you form? Note that a point cannot belong to multiple pairs.

Constraints

All input values are integers.

1 \leq N \leq 100

0 \leq a_i, b_i, c_i, d_i < 2N

a_1, a_2, ..., a_N, c_1, c_2, ..., c_N are all different.

b_1, b_2, ..., b_N, d_1, d_2, ..., d_N are all different.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
a_2 b_2
:
a_N b_N
c_1 d_1
c_2 d_2
:
c_N d_N

Output

Print the maximum number of friendly pairs.

Sample Input 1

3
2 0
3 1
1 3
4 2
0 4
5 5

Sample Output 1

2

For example, you can pair (2, 0) and (4, 2), then (3, 1) and (5, 5).

Sample Input 2

3
0 0
1 1
5 2
2 3
3 4
4 5

Sample Output 2

2

For example, you can pair (0, 0) and (2, 3), then (1, 1) and (3, 4).

Sample Input 3

2
2 2
3 3
0 0
1 1

Sample Output 3

0

It is possible that no pair can be formed.

Sample Input 4

5
0 0
7 3
2 2
4 8
1 6
8 5
6 9
5 4
9 1
3 7

Sample Output 4

5

Sample Input 5

5
0 0
1 1
5 5
6 6
7 7
2 2
3 3
4 4
8 8
9 9

Sample Output 5

4

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::char::from_digit;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;
 
type BoxResult<T> = Result<T, Box<std::error::Error>>;
 
fn main() {
    let mut scanner = Scanner::new(stdin());
    let n = scanner.read::<usize>().unwrap();
    let mut reds = vec![];
    let mut blues = vec![];
    for i in 0..n {
        let line = scanner.read_vector::<usize>().unwrap();
        let (a, b) = (line[0], line[1]);
        reds.push((a, b, i));
    }
    for i in 0..n {
        let line = scanner.read_vector::<usize>().unwrap();
        let (c, d) = (line[0], line[1]);
        blues.push((c, d, n + i));
    }
    let mut adj = AdjacencyList::new(2 * n + 2);
    for &(a, b, i) in reds.iter() {
        for &(c, d, j) in blues.iter() {
            if a < c && b < d {
                adj.add_edge(i, j, 1, 0, 0);
            }
        }
    }
    for i in 0..n {
        adj.add_edge(2 * n, i, 1, 0, 0);
        adj.add_edge(n + i, 2 * n + 1, 1, 0, 0);
    }
    let ans = maximal_flow(2 * n, 2 * n + 1, &mut adj);
    println!("{}", ans);
}
 
type Cost = i64;
type Capacity = i64;
type Vertex = usize;
type Index = usize;
 
#[derive(Clone, Copy, Debug, PartialEq)]
struct Edge {
    to: usize,
    cap: i64,
    cost: i64,
    rev: usize,
}
 
#[derive(Clone, Debug)]
struct AdjacencyList {
    len: usize,
    lists: Vec<Vec<Edge>>,
}
 
impl AdjacencyList {
    fn new(len: usize) -> AdjacencyList {
        AdjacencyList { len: len, lists: vec![vec![]; len] }
    }
 
    fn add_edge(&mut self, from: Vertex, to: Vertex, cap: Capacity, cost: Cost, rev_cap: Capacity) {
        let (from_dim, to_dim) = (self.lists[from].len(), self.lists[to].len());
        self.lists[from].push(Edge {
            to: to,
            cap: cap,
            cost: cost,
            rev: to_dim,
        });
        self.lists[to].push(Edge {
            to: from,
            cap: rev_cap,
            cost: -cost,
            rev: from_dim,
        });
    }
 
    fn len(&self) -> usize {
        self.len
    }
}
 
 
fn maximal_flow(src: Vertex, snk: Vertex, adj: &mut AdjacencyList) -> Capacity {
    let mut flow = 0;
    while let Some(path) = dfs(src, snk, &adj) {
        let min_cap = path.iter().fold(std::i64::MAX, |acc, &(v, i)| min(adj.lists[v][i].cap, acc));
        for &(v, i) in path.iter() {
            adj.lists[v][i].cap -= min_cap;
            let (to, rev) = (adj.lists[v][i].to, adj.lists[v][i].rev);
            adj.lists[to][rev].cap += min_cap;
        }
        flow += min_cap;
    }
    flow
}
 
fn dfs(src: usize, snk: usize, adj: &AdjacencyList) -> Option<Vec<(Vertex, Index)>> {
    let mut used = vec![false; adj.len()];
    let mut stack = VecDeque::new();
    let mut used_stack = VecDeque::new();
    stack.push_front((src, src, 0));
    while stack.len() > 0 {
        let tuple = stack.pop_front().unwrap();
        let (crt, _prv, _index) = (tuple.0, tuple.1, tuple.2);
        if used[crt] {
            continue;
        }
        used[crt] = true;
        used_stack.push_front(tuple);
        if crt == snk {
            break;
        }
        for (i, ref e) in adj.lists[crt].iter().enumerate() {
            if e.cap == 0 || used[e.to] {
                continue;
            }
            stack.push_front((e.to, crt, i));
        }
    }
 
    let mut tb = used_stack.pop_front().unwrap();
    if tb.0 != snk {
        return None;
    }
    let mut path = vec![(tb.1, tb.2)];
    while tb.1 != src {
        let new_tb = used_stack.pop_front().unwrap();
        if new_tb.0 != tb.1 {
            continue;
        }
        tb = new_tb;
        path.push((tb.1, tb.2));
    }
    path.reverse();
    Some(path)
}
 
 
 
#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
 
    #[allow(dead_code)]
    fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
 
    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    #[allow(dead_code)]
    fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}