Buggy python submission (verdict: Runtime Error):
from collections import Counter
from itertools import permutations

N = int(input())
x, y = (
    zip(*(map(int, input().split()) for _ in range(N))) if N else
    ((), ())
)

# (p, q) = (x_i - x_j, y_i - y_j) を満たす組(i, j)の個数が最大となるように
# p, qを定めればよい
D = Counter(
    (x[i] - x[j], y[i] - y[j])
    for i, j in permutations(range(N), 2)
)
ans = N - max(D.values())

print(ans)


Fixed submission:
N = int(input())
x, y = (
    zip(*(map(int, input().split()) for _ in range(N))) if N else
    ((), ())
)

class UnionFindTree:
    def __init__(self, n):
        self.p = [i for i in range(n + 1)]
        self.r = [0 for _ in range(n + 1)]

    def find(self, x):
        if self.p[x] != x:
            self.p[x] = self.find(self.p[x])
        return self.p[x]

    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px != py:
            if self.r[px] < self.r[py]:
                self.p[px] = py
            else:
                self.p[py] = px
                if self.r[px] == self.r[py]:
                    self.r[px] += 1

    def same(self, x, y):
        return self.find(x) == self.find(y)


ans = 10**10

for i in range(N):
    for j in range(N):
        p, q = (x[i] - x[j], y[i] - y[j])
        uft = UnionFindTree(N)
        for u in range(N - 1):
            for v in range(u + 1, N):
                if (x[u] - x[v], y[u] - y[v]) == (p, q) or (x[u] - x[v], y[u] - y[v]) == (-p, -q):
                    uft.union(u, v)
        ans = min(ans, len({uft.find(z) for z in range(N)}))

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
x, y = (
    zip(*(map(int, input().split()) for _ in range(N))) if N else
    ((), ())
)

class UnionFindTree:
    def __init__(self, n):
        self.p = [i for i in range(n + 1)]
        self.r = [0 for _ in range(n + 1)]

    def find(self, x):
        if self.p[x] != x:
            self.p[x] = self.find(self.p[x])
        return self.p[x]

    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px != py:
            if self.r[px] < self.r[py]:
                self.p[px] = py
            else:
                self.p[py] = px
                if self.r[px] == self.r[py]:
                    self.r[px] += 1

    def same(self, x, y):
        return self.find(x) == self.find(y)


ans = 10**10

for i in range(N):
    for j in range(N):
        p, q = (x[i] - x[j], y[i] - y[j])
        uft = UnionFindTree(N)
        for u in range(N):
            for v in range(N):
                if (x[u] - x[v], y[u] - y[v]) == (p, q) or (x[u] - x[v], y[u] - y[v]) == (-p, -q):
                    uft.union(u, v)
        ans = min(ans, len({uft.find(z) for z in range(N)}))

print(ans)


Fixed submission:
N = int(input())
x, y = (
    zip(*(map(int, input().split()) for _ in range(N))) if N else
    ((), ())
)

class UnionFindTree:
    def __init__(self, n):
        self.p = [i for i in range(n + 1)]
        self.r = [0 for _ in range(n + 1)]

    def find(self, x):
        if self.p[x] != x:
            self.p[x] = self.find(self.p[x])
        return self.p[x]

    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px != py:
            if self.r[px] < self.r[py]:
                self.p[px] = py
            else:
                self.p[py] = px
                if self.r[px] == self.r[py]:
                    self.r[px] += 1

    def same(self, x, y):
        return self.find(x) == self.find(y)


ans = 10**10

for i in range(N):
    for j in range(N):
        p, q = (x[i] - x[j], y[i] - y[j])
        uft = UnionFindTree(N)
        for u in range(N - 1):
            for v in range(u + 1, N):
                if (x[u] - x[v], y[u] - y[v]) == (p, q) or (x[u] - x[v], y[u] - y[v]) == (-p, -q):
                    uft.union(u, v)
        ans = min(ans, len({uft.find(z) for z in range(N)}))

print(ans)