Fair value after two informed buys

A stock is worth either $100 or $110, each equally likely a priori. Of the order flow, $40\%$ is informed (buys if the true value is $110, sells if $100); the other $60\%$ is uninformed and buys or sells with equal probability. Two orders arrive one after another and both are buys (each trader acts independently given the true value). Conditioned on seeing both buys, what is the fair value of the stock now (in dollars, to two places)?