Largest Sunflower

A gardener plants a row of 8 sunflowers whose heights are i.i.d. continuous random variables (so all heights are distinct with probability 1). Walking along the row from left to right, the gardener keeps a sunflower if and only if it is taller than every sunflower seen so far (the first sunflower is always kept).

What is the expected number of sunflowers kept? Give the exact value as a fraction.