def General_Binary_Increase_Search_Integer(L, R, cond, default=None):
    """ 条件式が単調増加であるとき, 整数上で二部探索を行う.

    L: 解の下限
    R: 解の上限
    cond: 条件(1変数関数, 広義単調増加を満たす)
    default: Lで条件を満たさないときの返り値
    """

    if not(cond(R)):
        return default

    if cond(L):
        return L

    R+=1
    while R-L>1:
        C=L+(R-L)//2
        if cond(C):
            R=C
        else:
            L=C
    return R

#==================================================
def solve():
    N=int(input())

    X=[0]*N; Y=[0]*N; T=[0]*N
    for i in range(N):
        X[i],Y[i],T[i]=map(int,input().split())

    level=[[0]*N for _ in range(N)]
    for i in range(N):
        level_i=level[i]
        for j in range(N):
            if T[i]==T[j]:
                dx=X[i]-X[j]
                dy=Y[i]-Y[j]
                level_i[j]=dx*dx+dy*dy
            else:
                ri=X[i]*X[i]+Y[i]*Y[i]
                rj=X[j]*X[j]+Y[j]*Y[j]
                if ri<rj:
                    ri,rj=rj,ri

                check=lambda k:ri-k-rj<=0 or (ri-k-rj)**2<=4*k*rj
                level_i[j]=General_Binary_Increase_Search_Integer(0,10**9,check)

    inf=float("inf")
    D=[inf]*N; D[0]=0
    F=[0]*N

    for _ in range(N):
        i=-1
        for p in range(N):
            if F[p]==0 and (i==-1 or D[p]<D[i]):
                i=p

        F[i]=1
        level_i=level[i]
        for j in range(N):
            if F[j]==0 and max(D[i],level_i[j])<D[j]:
                D[j]=max(D[i],level_i[j])

    return D[N-1]

#==================================================
from math import sqrt

print(solve())