Major Infection

You are given an array $A$ of length $N$. You can perform the following operation on it: - Choose a non-empty contiguous subarray $A[L\ldots R]$ of $A$ that has a *majority element*$^\dagger$. - Let $M$ be this majority element. Then, set $A_L = A_{L+1} = \ldots = A_R = M$. Find the lexicographically minimum array that can be attained as a result of performing the given operation however many