  In this paper we study the scattering amplitudes at strong coupling for the
case where the number of gluons is a multiple of four. This is an important
missing piece in arXiv:1002.2459. The tricky point for n=4K is that there is
some accidental degeneracy in such case. We explain this point in detail and
show that a non-trivial monodromy around infinity was developed by the
world-sheet coordinate transformation appearing in the computation. It turns
out that besides solving the Y system, we also need to calculate T functions to
compute the full amplitudes. We show that the T functions can be derived by
taking a limit of Y functions of a higher-point case. As a check, we obtain the
known result of eight-point in AdS_3 case.
