Forty teams play a tournament in which every team plays every other team exactly once. No ties occur, and each team has a \(50 \%\) chance of winning any game it plays. The probability that no two teams win the same number of games is \(m/n,\) where \(m_{}\) and \(n_{}\) are relatively prime positive integers. Find \(\log_2 n.\)
(第十七届AIME1999 第13题)