USACO 2022 Dec Silver 2. Circular Barn: May you help me understand this test case?

Problems and Contests
#1

The test case is :
1
100
78 38 78 36 62 78 22 74 64 80 80 28 4 60 70 6 4 56 50 66 96 50 64 74 86 62 12 44 16 28 24 48 74 78 6 2 60 92 34 70 16 14 34 28 96 36 62 94 36 94 60 58 54 36 24 78 18 46 62 60 60 30 16 88 36 44 4 40 66 56 12 14 30 54 72 52 14 10 8 30 90 12 28 46 6 8 42 78 88 4 56 92 96 54 100 40 60 40 88 28

The grader states that FJ should win, but why?
The first room that someone wins in is the first room with 4 cows in it (FJ takes 1, 2, or 3 cows and then FN takes the rest), so the winner should be FN…

#2

The game ends when there are zero cows in the current room just before a farmer goes. Reducing the number of cows to zero in a room doesn’t end the game if the farmers move to the next room immediately after that.

#3

Omg sry for late response; thank u so much!!! ^^ ^>^