Given the following context:

Briarcliff High School offers intramural sports and fields junior varsity and varsity teams in sixteen sports as the Briarcliff Bears. During the 38 years that Pace University operated its Briarcliff campus, it maintained fourteen intercollegiate varsity sports teams which played at the National Collegiate Athletic Association's (NCAA) Division II level.Briarcliff Manor has a history of auto racing. The First American International Road Race, sponsored by the village, centered around it. The prize, the Briarcliff Trophy valued at over $10,000 ($278,900 in 2018), was donated and presented by Walter Law. The race began at 4:45 a.m. on April 24, 1908 at the front of the Briarcliff Lodge and ending at the village grandstand. The winner, Arthur Strang in an Isotta Fraschini, covered the 240 miles (390 km) in five hours and fourteen minutes. More than 300,000 people watched the race, and the village had more than 100,000 visitors that day.On November 12, 1934, the Automobile Racing Club of America held another road race in Briarcliff Manor. The 100-mile (160 km) race was won by Langdon Quimby, driving a Willys 77, in a time of two hours and seven minutes. The race was held again on June 23, 1935; Quimby won again, four minutes faster than the previous year. In 1977, during the village's 75th anniversary, fifteen old racing cars participated in a motorcade around the 1934 race's route. In 2008, the village commemorated the first race's centennial in a parade featuring about 60 antique cars.

answer the following question:

Which race was held again on June 23, 1935? 

The 100-mile (160 km) race