Iga Swiatek and Daniil Medvedev, the last two former champions left in the U.S. Open singles draws after a series of upsets, swept into the quarterfinals at Flushing Meadows with a minimum of fuss on Monday.

Top seed Swiatek, who won the title two years ago, showcased her all-court game in a straightforward 6-4 6-1 win over Russian Liudmila Samsonova to open the evening session at Arthur Ashe Stadium and warned she was only going to improve.

"At the beginning, it wasn't easy to get the rhythm, especially because we kind of put our focus more on recovery than actually practicing before the slam," Swiatek said of her week in New York.