n=int(input())
x=[0]
y=[0]
t=[0]
for i in range(n):
    a,b,c=map(int,input().split())
    x.append(a)
    y.append(b)
    t.append(c)
def dist2(i,j,s):
    if t[i]==t[j]:
        return (x[i]-x[j])**2+(y[i]-y[j])**2<=s
    ri2=x[i]**2+y[i]**2
    rj2=x[j]**2+y[j]**2
    if ri2+rj2-s<0:return True
    return (ri2+rj2-s)**2<=4*ri2*rj2

def f(s):
    if s<0:return -1
    root=[[] for i in range(n+3)]
    for i in range(1,n+1):
        for j in range(i+1,n+1):
            if dist2(i,j,s):
                root[i].append(j)
                root[j].append(i)
    seen=[0]*(n+3)
    seen[1]=1
    data=[1]
    while data:
        now=data.pop()
        for to in root[now]:
            if seen[to]:continue
            seen[to]=1
            data.append(to)
    return seen[n]
ng=-1
ok=10**10
while ok-ng>1:
    mid=(ok+ng)//2
    if f(mid):ok=mid
    else:ng=mid
print(ok)