from math import sqrt

class UnionFind(object):
    def __init__(self, n=1):
        self.par = [i for i in range(n)]
        self.rank = [0 for _ in range(n)]
        self.size = [1 for _ in range(n)]

    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            self.par[x] = self.find(self.par[x])
            return self.par[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if x != y:
            if self.rank[x] < self.rank[y]:
                x, y = y, x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.par[y] = x
            self.size[x] += self.size[y]

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

    def get_size(self, x):
        x = self.find(x)
        return self.size[x]

def dist1(i, j):
    return (X[i] - X[j]) ** 2 + (Y[i] - Y[j]) ** 2

def dist2(i, j):
    return abs(sqrt(X[i] ** 2 + Y[i] ** 2) - sqrt(X[j] ** 2  + Y[j] ** 2))

N = int(input())
X, Y, T = [0] * N, [0] * N, [0] * N
for i in range(N):
    X[i], Y[i], T[i] = map(int, input().split())
    
yes = 10 ** 18 + 5
no = -1
eps = 10**-8
while yes - no != 1:
    mid = (yes + no)//2
    U = UnionFind(N)
    for i in range(N):
        for j in range(i + 1, N):
            if T[i] != T[j]:
                if dist2(i, j) ** 2 - eps <= mid:
                    U.union(i, j)
            else:
                if dist1(i, j) <= mid:
                    U.union(i, j)
    if U.is_same(0, N - 1):
        yes = mid
    else:
        no = mid
        
print(yes)