Take small example n=8.Smallest element in array A=1
A=2,3,8,1,5,4,7,6
Pair them:(2,3)(8,1)(5,4)(7,6)
Round 1 winner:2,1,4,6.
Pair them for round 2: (2,1)(4,6)
Round 2 winner: 1,4
Round 3 winner:1
Elements who lost to smallest element 1=8,2,4.
Total no of element who lost to first smallest element=log(n)