  Collinear limit usually provides strong constraints for scattering
amplitudes. At strong coupling, collinear limit of the amplitudes in N=4 SYM is
related to the large mass limit of the corresponding Y system. In this paper,
we consider a special case in which all mass parameters are taken to be large,
which corresponds to a multi-double-collinear limit in which a n-side polygon
becomes pentagons. This limit provides a useful constraint for amplitudes, in
particular, can be used to fix the periods part for the case of 4K gluons,
which is the last missing piece of full amplitudes.
