Maximum Number of Colinear Points

#include <bits/stdc++.h>
using namespace std;
 
pair<pair<int, int>, int> get_line(pair<int, int> a, pair<int, int> b) {
	pair<int, int> z = {b.first - a.first, b.second - a.second};
	swap(z.first, z.second);
 
	z.first *= -1;
	int g = __gcd(z.first, z.second);
	z.first /= g;
	z.second /= g;
 
	z = min(z, {-z.first, -z.second});
	return {z, z.first * a.first + z.second * a.second};
}
 
int main() {
	int n;
	while (cin >> n) {
		if (n == 0) { break; }
 
		vector<pair<int, int>> points(n);
		for (int i = 0; i < n; i++) { cin >> points[i].first >> points[i].second; }
		map<pair<pair<int, int>, int>, int> collinear_count;
		for (int i = 0; i < n; i++) {
			for (int j = i + 1; j < n; j++) {
				collinear_count[get_line(points[i], points[j])]++;
			}
		}
 
		int mx = 0;
		for (auto x : collinear_count) { mx = max(mx, x.second); }
		int res = 0;
		for (int i = 1; i <= n; i++) {
			if (i * (i - 1) / 2 <= mx) { res = i; }
		}
 
		cout << res << '\n';
	}
}

import math
from collections import defaultdict
from typing import Tuple
 
 
def get_line(a: Tuple[int, int], b: Tuple[int, int]) -> Tuple[Tuple[int, int], int]:
	z = (b[0] - a[0], b[1] - a[1])
	z = (-z[1], z[0])
 
	g = math.gcd(z[0], z[1])
	z = (z[0] // g, z[1] // g)
 
	z = min(z, (-z[0], -z[1]))
 
	c = z[0] * a[0] + z[1] * a[1]
	return (z, c)
 
 
while True:
	n = int(input())
	if n == 0:
		break
 
	points = []
	for _ in range(n):
		x, y = map(int, input().split())
		points.append((x, y))
 
	collinear_count = defaultdict(int)
 
	for i in range(n):
		for j in range(i + 1, n):
			collinear_count[get_line(points[i], points[j])] += 1
 
	mx = max(collinear_count.values(), default=0)
 
	res = 0
	for i in range(1, n + 1):
		if i * (i - 1) // 2 <= mx:
			res = i
 
	print(res)