At what point is a June rate increase priced in to the EUR/USD?

Is a June increase priced in at this point?

What would the Core CPI report need to be to cause the market to think there might be rate increases beyond June?

With fed fund futures priced at >90% certainty, I would wager that the hike is pretty well priced into all markets at this point. CPI isn't going to make any difference with regard to this or future increases. We need Q2 preliminary GDP, the next NFP, and the fed statement for June to start pricing any future meetings...