Rough rule of thumb, a consumer-grade directional antenna (at least at the time, maybe they've improved in the last 10yrs) will give your signal strength a one-digit multiplier (say ~8x), meaning ~7-10dB. But that n^2 means that improvement only takes you 2-3x farther, not 8x.
Here we're talking about ~100x the distance, which would need a 10000x = 40dB improvement in signal strength. AFAIK an antenna like that would cost more than the entire city block where I grew up