Input Matching Network Design for Bilateral LNA with Given S-Parameters and Noise Figure

I am a senior undergrad student, and I've been toiling over a homework assignment for days. I am designing a high-frequency Low Noise Amplifier with the following parameters (see attached images to get a better idea of the design):
S11=0.7@-105deg
S12=0.11@20deg
S21=3@75deg
S22=0.46@-70deg
Fmin=0.8dB
optimum reflection coefficient= 0.7@55deg
Rn=0.8ohms

After Smith chart analyses with the Operating Gain circles, Noise circles, and VSWR circle, I settle on the following parameters:
F=0.85dB
Gp=30
VSWR_in=4.5
gamma_in_a=0.6339@-119.74deg
gamma_s=0.4@121deg
gamma_in=0.82474@-120.48deg
gamma_l=0.55303@87.52deg
gamma_out=conj(gamma_l)

My problem is that I don't know how to design an input matching network for this LNA because |gamma_in_a| does not equal |gamma_s|. Also |gamma_s| does not equal |gamma_in|.

I am interested in such a question too and I will wait here for some competent answers if you don't mind

I am unfamiliar with F=0.85dB and Gp=30. Could you explain what these are? I would expect |gamma_in_a| to differ from |gamma_s|, as that difference is the reason to have matching network MNs.

gamma_in is the refelction coefficient at the input of the device that results in optimum noise performance.

The job of the matching metwork is to make the 50 ohm source "look like" this impedance at the input of the device. The device will not be perfectly matched to the source.

Convert the reflection coefficient to an impedance by 50 x (1+gamma)/(1-gamma) in the usual way
plot this impedance on the smith chart, insert whatever matching elements are needed to get from 50R to this point.

Done.

Because there is an an intenional mis-match between this network and the input of the device, this will result in an imperfect match at the input of the LNA ... but that's OK, that is to be expected when designing for minimum noise rather than maximum gain.