Farmer
John‘s N cows (1 <= N <= 100,000) are out exercising their hooves
again, jogging along an infinite track. Each cow starts at a distinct
position on the track, and some cows run at different speeds.
The track is divided into lanes so that
cows may move past each other. No two cows in the same lane may ever
occupy the same position. Farmer John doesn‘t want any cow to have to
change lanes or adjust speed, and he wonders how many lanes he will need
to accomplish this if the cows are going to run for T minutes (1 <= T
<= 1,000,000,000).