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use std::{
    cmp::Ordering,
    ops::{Add, AddAssign, Sub},
};

#[derive(Clone, Copy, Eq, PartialEq, Debug, Hash)]
pub struct Point {
    pub row: u32,
    pub column: u32,
}

impl Point {
    pub fn new(row: u32, column: u32) -> Self {
        Self { row, column }
    }

    pub fn zero() -> Self {
        Point::new(0, 0)
    }

    pub fn is_zero(&self) -> bool {
        self.row == 0 && self.column == 0
    }
}

impl<'a> Add<&'a Self> for Point {
    type Output = Point;

    fn add(self, other: &'a Self) -> Self::Output {
        if other.row == 0 {
            Point::new(self.row, self.column + other.column)
        } else {
            Point::new(self.row + other.row, other.column)
        }
    }
}

impl<'a> Sub<&'a Self> for Point {
    type Output = Point;

    fn sub(self, other: &'a Self) -> Self::Output {
        debug_assert!(*other <= self);

        if self.row == other.row {
            Point::new(0, self.column - other.column)
        } else {
            Point::new(self.row - other.row, self.column)
        }
    }
}

impl<'a> AddAssign<&'a Self> for Point {
    fn add_assign(&mut self, other: &'a Self) {
        if other.row == 0 {
            self.column += other.column;
        } else {
            self.row += other.row;
            self.column = other.column;
        }
    }
}

impl PartialOrd for Point {
    fn partial_cmp(&self, other: &Point) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

impl Ord for Point {
    fn cmp(&self, other: &Self) -> Ordering {
        let a = (self.row as usize) << 32 | self.column as usize;
        let b = (other.row as usize) << 32 | other.column as usize;
        a.cmp(&b)
    }
}