import math
I,R,S=input,range,math.sqrt
def J():
	return map(int,I().split())
N=int(I())
D=[0]*N
for i in R(N):
	X,Y,T=J()
	D[i]=[X*X+Y*Y,X,Y,T,i]
D.sort()
for i in R(N):
	j=D[i][4]
	if j<1:o=i
	if j>N-2:n=i
if n<o:o,n=n,o
s=0
i=o
while i<n:
	t,j=3200000001,i+1
	d=D[i]
	while j<=n:
		if d[3]!=D[j][3]:break
		u=(D[j][1]-d[1])**2+(D[j][2]-d[2])**2
		if t>u:i,t=j,u
		j=j+1
	if j<=n:
		l=D[j][0]
		p=4*l*d[0]
		r=int(math.sqrt(p))+1
		while p<r**2:r-=1
		u=l+d[0]-r
		if t>u:i,t=j,u
	s=max(s,t)
print(s)