###########

def moyenne(l, cent):
    n = len(l)
    if n == 0:return float("inf")
    s = 0
    for i in range(n):
        s += distance(cent, l[i])
    return s/n


def centroide(l):
    if len(l) == 0:return [0,0]
    xs = 0
    ys = 0
    for p in l:
        xs += p[0]
        ys += p[1]

    return [xs/len(l),ys/len(l)]


def distance(p1,p2):
    i = p1[0] - p2[0]
    j = p1[1] - p2[1]
    return sqrt(i*i + j*j)

def metrique(z):
    somme = 0
    for i in range(len(z)):
        formule = []
        centI = centroide(z[i])
        sigmaI = moyenne(z[i], centI)
        for j in range(len(z)):
            if (i==j):continue
            centJ = centroide(z[j])
            sigmaJ = moyenne(z[j], centJ)
            d = distance(centI,centJ)
            # division par 0
            if  d > 1e-8:
                formule.append((sigmaI+sigmaJ)/d)
            else:
                return float("inf")
        if formule:
            somme += max(formule)

    return somme/7