import sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
yes = lambda :print("yes");Yes = lambda :print("Yes");YES = lambda : print("YES")
no = lambda :print("no");No = lambda :print("No");NO = lambda : print("NO")
#######################################################################

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
 
    def __str__(self):
        return '\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())


n = ni()

x,y,t = zip(*[na() for i in range(n)])

ok = 10**10
ng = -1

while ok - ng > 1:
    d = ok+ng>>1
    uf = UnionFind(n)
    for i in range(n):
        for j in range(i+1, n):
            if t[i] == t[j]:
                if (x[i]-x[j])**2+(y[i]-y[j])**2 <= d:
                    uf.union(i, j)
            else:
                d1, d2 = min(x[i]**2+y[i]**2,x[j]**2+y[j]**2),max(x[i]**2+y[i]**2,x[j]**2+y[j]**2)
                #print(d1,d2)
                if (d1 + d2 - d)**2 <= 4 * d1 *d2 or d1 + d2 - d <= 0:
                    uf.union(i, j)
    #print(d, uf.all_group_members())
    if uf.same(0, n-1):
        ok = d
    else:
        ng = d
print(ok)