Novak Djokovic, birthday boy Rafael Nadal and Roger Federer all reached the third round of the French Open on Thursday, while the race for the women’s title was thrown wide open after world No. 1 Ash Barty limped out.

Djokovic, the top seed on the men’s side, continued his bid for his second French Open title and 19th Grand Slam with a straight-sets win over Uruguay’s Pablo Cuevas.

The 34-year-old, who is looking to become the first man in over 50 years to win all four Grand Slams multiple times, won 6-3, 6-2, 6-4.

“I stayed concentrated,” Djokovic said. “I thought the third set was very difficult for me because he lifted the level of his game.”

Djokovic will next face Lithuanian Ricardas Berankis.

World No. 3 Nadal, bidding for a 14th French Open and record-setting 21st Grand Slam title, celebrated his 35th birthday by defeating Richard Gasquet.

Nadal stormed to a 6-0, 7-5, 6-2 win in a match played at Court Philippe Chatrier, which was empty due to a 9 p.m. curfew in place because of COVID-19.

Gasquet won just nine points in the first set.

He managed a brief show of defiance — rallying from 2-5 down to get even at 5-5 in the second set — but eventually suffered his 17th defeat in 17 matches against the Spaniard.

“The important thing is winning the matches,” Nadal said. “If it’s in straight sets it’s better.”

“I don’t complain at all, the main thing is to feel myself playing well.”

Next up for Nadal is Britain’s Cameron Norrie — who he beat at this year’s Australian Open and on clay in Barcelona.

Gasquet’s loss means there are no Frenchmen or women in the third round for the first time.

Federer stayed on course for a quarterfinal showdown with Djokovic, but only after becoming entangled in a rare running dispute with the chair umpire.

The 20-time major winner and 2009 champion beat Marin Cilic for the 10th time in 11 meetings, winning 6-2, 2-6, 7-6 (7-4), 6-2.

Federer was handed a time violation by umpire Emmanuel Joseph while trailing 1-3 in the second set for taking too long between points in order to retrieve his towel.

“I don’t even dare to go my towel anymore,” he said to Joseph.

Federer, the oldest man in the draw at 39, continued to lose his cool and the set before recovering to defeat former world No. 3 Cilic.

“I had very good moments, in the tiebreak in particular, and I served really well to finish,” said Federer, who hit 47 winners.

Playing in only his second French Open since 2015, Federer moves on to face 59th-ranked German Dominik Koepfer.

Women’s No. 1 seed Barty was already suffering from a left hip injury when she retired midway through the second set of her second-round match against Poland’s Magda Linette.

The Australian, who won the title in her last visit to Roland Garros in 2019, left the court for medical treatment after losing the first set 6-1.

She then called it quits at 2-2 in the second set.

“It’s heartbreaking,” Barty said. “It’s a miracle I got past the first round.”

The 25-year-old’s withdrawal leaves the tournament without the world’s top three female players.

World No. 2 Naomi Osaka pulled out following a media boycott, saying she has suffered “bouts of depression” for three years.

Third-ranked Simona Halep, the 2018 French Open winner, withdrew before the event with an injury.

Defending champion Iga Swiatek eased into the third round with a 6-1, 6-1 win over Sweden’s Rebecca Peterson.

The eighth-seeded Pole goes on to face Estonian Anett Kontaveit for a place in the last 16.

Swiatek hasn’t dropped a set at Roland Garros in her last nine matches.

Elsewhere, fourth seed Sofia Kenin, the 2020 runner-up, saw off American compatriot Hailey Baptiste 7-5, 6-3.

Three-time quarterfinalist and fifth seed Elina Svitolina was similarly untroubled against Ann Li of the United States, winning 6-0, 6-4.

However, No. 9 seed Karolina Pliskova was eliminated by 2018 runner-up Sloane Stephens as the 59th-ranked American won 7-5, 6-1.

Spain’s Carlos Alcaraz, 18, became the youngest player to make the last 32 since Andrei Medvedev in 1992 when he defeated No. 28 seed Nikoloz Basilashvili 6-4, 6-2, 6-4.

Two Italian teens made it through with 18th-seeded Jannik Sinner seeing off compatriot Gianluca Mager while highly rated Lorenzo Musetti eliminated Yoshihito Nishioka.

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