def mask(c,a,b):
 m=0
 for z in c['pair']:
  if z==a: m+=1
  elif z==b: m+=2
 return m
def integ(basis,x): return all(v.denominator==1 and (v==0 or v==1) for v in x)
def obj(basis,x): return sum(c['cost']*x[k] for k,c in enumerate(basis))
base=cols[:7]
same=[c for c in roots if mask(c,a,b) in (0,3)]
pick=min([c for c in same if mask(c,a,b)==3],key=lambda c:c['cid'])
sc=[base[i] for i in range(7) if i!=a-1]+same
sb=[pick if i==a-1 else base[i] for i in range(7)]
u,sc,sb,sx,spi=runnode(sc,sb,a,b,1,u)
print('SAME',obj(sb,sx),integ(sb,sx),[(c['cid'],c['cov'],sx[k]) for k,c in enumerate(sb)])