Buggy python submission (verdict: Time Limit Exceeded):
class UF():
  def __init__(self, N):
    self._parent=[n for n in range(0, N)]
    self._size=[1] * N

  def find_root(self, x):
    if self._parent[x]==x:return x
    self._parent[x]=self.find_root(self._parent[x])
    return self._parent[x]

  def unite(self, x, y):
    gx=self.find_root(x)
    gy=self.find_root(y)
    if gx==gy:return

    if self._size[gx]<self._size[gy]:
      self._parent[gx]=gy
      self._size[gy]+=self._size[gx]
    else:
      self._parent[gy]=gx
      self._size[gx]+=self._size[gy]

  def size(self, x):
    return self._size[self.find_root(x)]

  def samegroup(self, x, y):
    return self.find_root(x)==self.find_root(y)

  def groupnum(self):
    N=len(self._parent)
    ans=0
    for i in range(N):
      if self.find_root(i)==i:
        ans+=1
    return ans

  def reset(self):
    self._parent=[n for n in range(0, n)]

n=int(input())
UF=UF(n)
l=[list(map(int,input().split())) for i in range(n)]
if n==1:
  print(1)
else:
  ans=[]
  for i in range(n):
    x1=l[i][0]
    y1=l[i][1]
    for j in range(n):
      if i!=j:
        x2=l[j][0]
        y2=l[j][1]
        p=x1-x2
        q=y1-y2
        for k1 in range(n):
          for k2 in range(n):
            if k1!=k2:
              if (l[k1][0]-p==l[k2][0] and l[k1][1]-q==l[k2][1]) or (l[k1][0]+p==l[k2][0] and l[k1][1]+q==l[k2][1]):
                UF.unite(k1,k2)
        ans.append(UF.groupnum())
        UF.reset()
  print(min(ans))

Fixed submission:
class UF():
  def __init__(self, N):
    self._parent=[n for n in range(0, N)]
    self._size=[1] * N

  def find_root(self, x):
    if self._parent[x]==x:return x
    self._parent[x]=self.find_root(self._parent[x])
    return self._parent[x]

  def unite(self, x, y):
    gx=self.find_root(x)
    gy=self.find_root(y)
    if gx==gy:return

    if self._size[gx]<self._size[gy]:
      self._parent[gx]=gy
      self._size[gy]+=self._size[gx]
    else:
      self._parent[gy]=gx
      self._size[gx]+=self._size[gy]

  def size(self, x):
    return self._size[self.find_root(x)]

  def samegroup(self, x, y):
    return self.find_root(x)==self.find_root(y)

  def groupnum(self):
    N=len(self._parent)
    ans=0
    for i in range(N):
      if self.find_root(i)==i:
        ans+=1
    return ans

  def reset(self):
    self._parent=[n for n in range(0, n)]

n=int(input())
UF=UF(n)
l=[list(map(int,input().split())) for i in range(n)]
if n==1:
  print(1)
else:
  ans=[]
  for i in range(n):
    x1=l[i][0]
    y1=l[i][1]
    for j in range(n):
      if i!=j:
        x2=l[j][0]
        y2=l[j][1]
        p=x1-x2
        q=y1-y2
        for k1 in range(n):
          for k2 in range(n):
            if k1!=k2:
              if (l[k1][0]-p==l[k2][0] and l[k1][1]-q==l[k2][1]) or (l[k1][0]+p==l[k2][0] and l[k1][1]+q==l[k2][1]):
                UF.unite(k1,k2)
        ans.append(UF.groupnum())
        UF.reset()
  print(min(ans))

Buggy python submission (verdict: Runtime Error):
import copy
n=int(input())
l=[list(map(int,input().split())) for i in range(n)]
ans=[]
for i in range(n):
  x1=l[i][0]
  y1=l[i][1]
  for j in range(n):
    if i!=j:
      x2=l[j][0]
      y2=l[j][1]
      if (x1-x2)!=0:
        p=(y1-y2)/(x1-x2)
        L=[]
        for k in range(n):
          L.append(round(l[k][1]-l[k][0]*p,9))
        ans.append(len(set(L)))
      else:
        L=[]
        for k in range(n):
          L.append(l[k][0])
        ans.append(len(set(L)))
print(min(ans))

Fixed submission:
class UF():
  def __init__(self, N):
    self._parent=[n for n in range(0, N)]
    self._size=[1] * N

  def find_root(self, x):
    if self._parent[x]==x:return x
    self._parent[x]=self.find_root(self._parent[x])
    return self._parent[x]

  def unite(self, x, y):
    gx=self.find_root(x)
    gy=self.find_root(y)
    if gx==gy:return

    if self._size[gx]<self._size[gy]:
      self._parent[gx]=gy
      self._size[gy]+=self._size[gx]
    else:
      self._parent[gy]=gx
      self._size[gx]+=self._size[gy]

  def size(self, x):
    return self._size[self.find_root(x)]

  def samegroup(self, x, y):
    return self.find_root(x)==self.find_root(y)

  def groupnum(self):
    N=len(self._parent)
    ans=0
    for i in range(N):
      if self.find_root(i)==i:
        ans+=1
    return ans

  def reset(self):
    self._parent=[n for n in range(0, n)]

n=int(input())
UF=UF(n)
l=[list(map(int,input().split())) for i in range(n)]
if n==1:
  print(1)
else:
  ans=[]
  for i in range(n):
    x1=l[i][0]
    y1=l[i][1]
    for j in range(n):
      if i!=j:
        x2=l[j][0]
        y2=l[j][1]
        p=x1-x2
        q=y1-y2
        for k1 in range(n):
          for k2 in range(n):
            if k1!=k2:
              if (l[k1][0]-p==l[k2][0] and l[k1][1]-q==l[k2][1]) or (l[k1][0]+p==l[k2][0] and l[k1][1]+q==l[k2][1]):
                UF.unite(k1,k2)
        ans.append(UF.groupnum())
        UF.reset()
  print(min(ans))