type LS = Vec<Vec<Option<u64>>>;

struct Lattice { ls: LS }

impl Lattice {
    pub fn new() -> Lattice {
        let mut ls = LS::new();
        for _i in 0..21 {
            let lr = vec![None; 21];
            ls.push(lr);
        }
        ls[0][0] = Some(1);
        Lattice { ls: ls }
    }
    pub fn compute(&mut self, i: usize, j: usize) -> u64 {
        if self.ls[i][j].is_some() { return self.ls[i][j].unwrap(); }
        let mut res = 0u64;
        if i > 0 { res += self.compute(i - 1, j); }
        if j > 0 { res += self.compute(i, j - 1); }
        self.ls[i][j] = Some(res);
        res
    }
}

fn main() {
    let mut lt = Lattice::new();
    let res = lt.compute(20, 20);
    println!("{}", res);
}