<p>Given an array of <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents a point on the <strong>X-Y</strong> plane, return <em>the maximum number of points that lie on the same straight line</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane1.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane2.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 300</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>All the <code>points</code> are <strong>unique</strong>.</li>
</ul>



def calc_sign(v: tuple[int, ...]) -> int:
    if v[0] > 0:
        return 1
    if v[0] < 0:
        return -1
    return calc_sign(v[1:])


def calc_gcd(v: list[int]) -> int:
    """
    v[0] > v[1] > ... > v[-1] > 0
    """
    if len(v) == 1:
        return v[0]
    r = v[0] % v[-1]
    if r == 0:
        return calc_gcd(v[1:])
    return calc_gcd(v[1:] + [r])


def coprimize(v: tuple[int, ...]) -> tuple[int, ...]:
    sign = calc_sign(v)
    gcd = calc_gcd([x for x in sorted(map(abs, v), reverse=True) if x > 0])
    return tuple(sign * x // gcd for x in v)


class Solution:
    def maxPoints(self, points: list[list[int]]) -> int:
        if len(points) == 1:
            return 1
        line_to_points: dict[tuple[float, ...], set[tuple[int, int]]] = {}
        for (x1, y1), (x2, y2) in combinations(points, r=2):
            t = coprimize((x2 - x1, y2 - y1, x1 * y2 - x2 * y1))
            if t not in line_to_points:
                line_to_points[t] = set()
            line_to_points[t].add((x1, y1))
            line_to_points[t].add((x2, y2))
        return max(map(len, line_to_points.values()))
40436