S = 32767
def f(h):
    total = sum(h)
    n = len(h)
    p = [ x / float(total) for x in h ]
    o = [ +max(x > 0, int(round(x * S))) for x in p ]
    errs = lambda: [ o[i] - S*p[i] for i in range(n) ]
    err = errs()
    xs = S - sum(o)
    def isorted(minv, rev):
        ii = [ i for i in range(n) if o[i] > minv ]
        ii.sort(key=lambda i: err[i], reverse=rev)
        return ii
    if xs >= 0:
        ei = isorted(0, False)
        for i in ei:
            if xs == 0 or err[i] >= 1: break
            xs -= 1
            o[i] += 1
        err = errs()
        nz = n - o.count(0)
        addall = xs / nz
        o = [ x and x + addall for x in o ]
        xs -= addall * nz
        for i in isorted(0, False)[:xs]: o[i] += 1
    else:
        xs = -xs
        while 1:
            not01 = n - o.count(0) - o.count(1)
            if xs < not01 or xs < 1: break
            addall = xs / nz
            o = [ x and max(x - addall, 1) for x in o ]
            xs = sum(o) - S
        for x in isorted(1, True)[:xs]:
            o[x] -= 1
    return o

def maketests():
    import random
    random.seed(0)
    t = []
    for _ in range(100):
        l = 1 + min(int(random.expovariate(1/100.)), 1000)
        t.append([int(random.expovariate(1/10.)) for _ in range(l)])
    return t

def score(hist, prob):
    return sum((p/float(0x7fff) - float(h)/sum(hist))**2 for h, p in zip(hist, prob))

print '%.17g' % sum(score(t, f(t)) for t in maketests())