python3 -c "import urllib.request,json
R=7
C=11
N=77
W=[]
for r in range(R):
 for c in range(C):
  W.append([u*C+v for u in range(max(0,r-1),min(R,r+2)) for v in range(max(0,c-1),min(C,c+2))])
L=[]
L.append('Minimize')
L.append(' obj: L')
L.append('Subject To')
for i in range(N):
 t=' c'+str(i)+': '
 for k in range(1,N+1):
  t=t+'x'+str(i)+'_'+str(k)+' '
 L.append(t+'= 1')
for k in range(1,N+1):
 t=' d'+str(k)+': '
 for i in range(N):
  t=t+'x'+str(i)+'_'+str(k)+' '
 L.append(t+'= 1')
for q,w in enumerate(W):
 t=' w'+str(q)+': '
 for i in w:
  for k in range(1,N+1):
   t=t+str(k)+' x'+str(i)+'_'+str(k)+' + '
 L.append(t+'- L <= 0')
L.append('Bounds')
L.append(' L >= 0')
L.append('End')
s='\n'.join(L)
d=json.dumps(dict(model=s,format='lp')).encode()
req=urllib.request.Request('https://api.ceris.fyi/v1/solve',data=d,headers=dict(**{'Content-Type':'application/json','User-Agent':'Mozilla/5.0'}))
r=json.loads(urllib.request.urlopen(req,timeout=7).read().decode())
print(r.get('status'),r.get('objective_value'))
sol=r.get('solution',{})
nz=[]
for key,v in sol.items():
 f=float(v)
 if f>1e-7:
  nz.append((key,f))
print(len(nz))
frac=[q for q in nz if q[1]<0.999999]
print('frac',len(frac))
print(frac[:200])"