def solve():
    from math import sqrt,ceil

    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=sqrt(X[i]*X[i]+Y[i]*Y[i])
                rj=sqrt(X[j]*X[j]+Y[j]*Y[j])
                dr=abs(ri-rj)
                level_i[j]=ceil(dr*dr)

    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]

#==================================================
print(solve())