THIEF AND ANGLE

Divya's watch of worth Rs10 cr is abducted by N thieves(1,2....i...N). The fight over the watch leads to a final decision that it should belong to the thief who wins a simple game. The rules of the game state that every thief registers a time in the format HH:MM:SS . Accordingly the average A of three clockwise angles between the hours , minutes and seconds hands is calculated . Thus the ith thief