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_macros)]
macro_rules! input_byline {
    ($($r:tt)* ) => {
        let stdin = std::io::stdin();
        let mut q = std::collections::VecDeque::new();
        let mut next = || {
            if q.is_empty() {
                let mut s = String::new();
                stdin.read_line(&mut s);
                for v in s.split_whitespace() {
                    q.push_back(v.to_string());
                }
            }
            q.pop_front().unwrap()
        };
        input_inner!{next, $($r)*}
    };

}

#[allow(unused_macros)]
macro_rules! input {
    ($($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")
    };
}

trait Printable {
    fn p(&self);
}

impl<T: std::fmt::Display> Printable for T {
    fn p(&self) {
        println!("{}", self);
    }
}

impl<T: std::fmt::Display> Printable for [T] {
    fn p(&self) {
        for i in 0..self.len() {
            if i != 0 {
                print!(" ");
            }
            print!("{}", self[i]);
        }
        println!("");
    }
}

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

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

// TODO: remove clone & copy?
#[derive(Clone, Copy)]
struct Edge {
    from: usize,
    to: usize,
    cap: usize,
}

struct Dinic {
    graph: Vec<Vec<Edge>>,
}

impl Dinic {
    pub fn new(n: usize) -> Dinic {
        let graph = vec![vec![]; n];
        Dinic { graph: graph }
    }

    fn add_edge(&mut self, from: usize, to: usize, cap: usize) {
        let from_size = self.graph[from].len();
        let to_size = self.graph[to].len();
        self.graph[from].push(Edge {
            from: to_size,
            to: to,
            cap: cap,
        });
        self.graph[to].push(Edge {
            from: from_size,
            to: from,
            cap: 0,
        })
    }

    fn bfs(&self, s: usize) -> Vec<Option<usize>> {
        let mut depth = vec![None; self.graph.len()];
        let mut queue = std::collections::VecDeque::new();
        depth[s] = Some(0);
        queue.push_front(s);

        while !queue.is_empty() {
            let p = queue.pop_back().unwrap();
            for &edge in &self.graph[p] {
                if edge.cap > 0 && depth[edge.to].is_none() {
                    depth[edge.to] = Some(depth[p].unwrap() + 1);
                    queue.push_front(edge.to);
                }
            }
        }

        depth
    }

    fn dfs(
        &mut self,
        pos: usize,
        t: usize,
        flow: usize,
        depth: &Vec<Option<usize>>,
        memo: &mut Vec<usize>,
    ) -> usize {
        if pos == t {
            return flow;
        }
        for i in memo[pos]..self.graph[pos].len() {
            let e = self.graph[pos][i];
            if e.cap > 0 && depth[pos].unwrap() < depth[e.to].unwrap_or(0) {
                let f = self.dfs(e.to, t, std::cmp::min(flow, e.cap), depth, memo);
                if f > 0 {
                    self.graph[pos][i].cap -= f;
                    self.graph[e.to][e.from].cap += f;
                    return f;
                }
            }
            // 先でもいい？
            memo[pos] += 1;
        }
        0
    }

    fn max_flow(&mut self, s: usize, t: usize) -> usize {
        let mut flow = 0;
        loop {
            let depth = self.bfs(s);
            if depth[t].is_none() {
                break;
            }
            let mut memo = vec![0; self.graph.len()];
            loop {
                let f = self.dfs(s, t, std::usize::MAX, &depth, &mut memo);
                if f == 0 {
                    break;
                }
                flow += f;
            }
        }
        flow
    }
}

fn main() {
    input! {
        n: usize,
        pa: [(usize, usize); n],
        pb: [(usize, usize); n],
    }

    let mut dinic = Dinic::new(2 * n + 2);
    for i in 0..n {
        dinic.add_edge(2 * n, i, 1);
        dinic.add_edge(n + i, 2 * n + 1, 1);
    }
    for i in 0..n {
        for j in 0..n {
            if pa[i].0 < pb[j].0 && pa[i].1 < pb[j].1 {
                dinic.add_edge(i, n + j, 1);
            }
        }
    }
    println!("{}", dinic.max_flow(2 * n, 2 * n + 1));
}