from decimal import Decimal

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


def is_ok(s):
    uf = UnionFind(N)
    hs = Decimal(s)**Decimal('0.5')
    for i,xyti in enumerate(XYT):
        for j,xytj in enumerate(XYT[i+1:],start=i+1):
            if not uf.same(i,j):
                if xyti[2]==xytj[2]:
                    xi,yi,ti = xyti
                    xj,yj,tj = xytj
                    if (xi-xj)**2+(yi-yj)**2<=s:
                        uf.union(i,j)
                else:
                    if IJD[i*N+j]<=hs:
                        uf.union(i,j)
    return uf.same(0,N-1)



N = int(input())
XYT = [list(map(int, input().split())) for _ in range(N)]
D = []
for i in range(N):
    D.append(Decimal(XYT[i][0]**2+XYT[i][1]**2)**Decimal('0.5'))

IJD = [0]*(N**2)
for i in range(N):
    for j in range(i+1,N):
        IJD[i*N+j]=abs(D[i]-D[j])
ng = -1
ok = 3200000001
while (abs(ok - ng) > 1):
    mid = (ok + ng) // 2
    if is_ok(mid):
        ok = mid
    else:
        ng = mid
print(ok)