from collections import defaultdict

class UnionFind():
  def __init__(self,n):
    self.n=n
    self.parents=[-1]*n

  def find(self,x):
    if self.parents[x]<0:
      return x
    else:
      self.parents[x]=self.find(self.parents[x])
      return self.parents[x]

  def union(self,x,y):
    x=self.find(x)
    y=self.find(y)

    if x==y:
      return

    if self.parents[x]>self.parents[y]:
      x,y=y,x

    self.parents[x]+=self.parents[y]
    self.parents[y]=x

  def size(self,x):
    return -self.parents[self.find(x)]

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

  def members(self,x):
    root=self.find(x)
    return [i for i in range(self.n) if self.find(i)==root]

  def roots(self):
    return [i for i, x in enumerate(self.parents) if x< 0]

  def group_count(self):
    return len(self.roots())

  def all_group_members(self):
    group_members=defaultdict(list)
    for member in range(self.n):
      group_members[self.find(member)].append(member)
    return group_members



n=int(input())
xyt=[]
for i in range(n):
  x,y,t=map(int,input().split())
  xyt.append((x,y,t))

dist=[[10**18]*n for i in range(n)]
def calc(a,b):
  a,b=min(a,b),max(a,b)
  #print(a,b)
  ng,ok=-1,10**20
  while abs(ng-ok)>1:
    mid=(ng+ok)//2
    if a+b-mid<0 or (a+b-mid)**2<=4*a*b:
      ok=mid
    else:
      ng=mid
  return ok


  
for i in range(n):
  for j in range(i+1,n):
    xi,yi,ti=xyt[i]
    xj,yj,tj=xyt[j]
    if ti!=tj:
      dist[i][j]=calc(xi*xi+yi*yi,xj*xj+yj*yj)
    else:
      dx=xi-xj
      dy=yi-yj
      dist[i][j]=dx*dx+dy*dy

ng,ok=-1,10**18
while abs(ng-ok)>1:
  mid=(ng+ok)//2
  uf=UnionFind(n)
  for i in range(n):
    for j in range(i+1,n):
      if dist[i][j]<=mid:
        uf.union(i,j)
  if uf.same(0,n-1):
    ok=mid
  else:
    ng=mid
print(ok)