Problem:
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The Maximum Number of Overlaps

Given a set of $N$ axis-aligned rectangular seals, find the number of overlapped seals on the region which has the maximum number of overlapped seals.

Input

The input is given in the following format.

$N$

$x1_1$ $y1_1$ $x2_1$ $y2_1$

$x1_2$ $y1_2$ $x2_2$ $y2_2$

:

$x1_N$ $y1_N$ $x2_N$ $y2_N$

($x1_i, y1_i$) and ($x2_i, y2_i$) are the coordinates of the top-left and the bottom-right corner of the $i$-th seal respectively.

Constraints

$ 1 \leq N \leq 100000 $

$ 0 \leq x1_i < x2_i \leq 1000 $

$ 0 \leq y1_i < y2_i \leq 1000 $

$ x1_i, y1_i, x2_i, y2_i$ are given in integers

Output

Print the maximum number of overlapped seals in a line.

Sample Input 1

2
0 0 3 2
2 1 4 3

Sample Output 1

2

Sample Input 2

2
0 0 2 2
2 0 4 2

Sample Output 2

1

Sample Input 3

3
0 0 2 2
0 0 2 2
0 0 2 2

Sample Output 3

3

Solution in Rust (judge verdict: Accepted)

fn main() {
    const W: usize = 1000;
    const H: usize = 1000;
    let mut a: [[i32; H + 1]; W + 1] = [[0; H + 1]; W + 1];
    let N:u32 = read_num();
    for i in 0..N {
        let v: Vec<usize> = read_nums();
        let (x1, y1, x2, y2) = (v[0], v[1], v[2], v[3]);
        a[x1][y1] += 1;
        a[x1][y2] -= 1;
        a[x2][y1] -= 1;
        a[x2][y2] += 1;
    }
    for i in 0..H+1 {
        for j in 0..W {
            a[i][j + 1] += a[i][j];
        }
    }
    for j in 0..W+1 {
        for i in 0..H {
            a[i + 1][j] += a[i][j];
        }
    }
    let mut result = 0;
    for i in 0..H {
        for j in 0..W {
            result = std::cmp::max(result, a[i][j]);
        }
    }
    println!("{}", result);
}

fn read_str() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}

fn read_num<T>() -> T where 
    T: std::str::FromStr,
    T::Err: std::fmt::Debug {
    read_str().trim().parse().unwrap()
}

fn read_nums<T>() -> Vec<T> where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug {
    let s = read_str();
    let a: Vec<&str> = s.split_whitespace().collect();
    let mut v: Vec<T> = Vec::new();
    for x in a {
        v.push(x.parse().unwrap());
    }
    v
}