You are given an array with $N$ elements. The values of the elements may be any number in the interval $[0,10^9]$. Define $f(a,b)$ as the bitwise or of all the values in the subarray $[a,b]$. Find a bound on the number of distinct values of $f(a,b)$.
Attempts: I have tried to brute force cases to find a pattern but was unsuccessful.
Please explain the reasoning behind your answer. I am a complete beginner.