import sys
input = sys.stdin.readline
from math import sqrt

N=int(input())
P=[list(map(int,input().split())) for i in range(N)]

OK=3200000000
NG=-1

while OK>NG+1:
    mid=(OK+NG)//2

    CAN=[0]*N
    CAN[0]=1

    Q=[0]
    while Q:
        x=Q.pop()

        x0,y0,t0=P[x]

        for i in range(N):
            if CAN[i]==1:
                continue

            x1,y1,t1=P[i]

            if t0==t1:
                dis=(x0-x1)**2+(y0-y1)**2

                if dis<=mid:
                    CAN[i]=1
                    Q.append(i)
                    
            else:
                a=(x1*x1+y1*y1)
                b=(x0*x0+y0*y0)

                if a+b-mid<0.8:
                    CAN[i]=1
                    Q.append(i)

                elif (a+b-mid)**2<=4*a*b:
                    CAN[i]=1
                    Q.append(i)

    #print(mid,CAN)

    if CAN[N-1]==1:
        OK=mid
    else:
        NG=mid

print(OK)