def process(r: int, right_min: float, right_max: float) -> None:
            p_max, pivot_index = prev_max[r]
            curr_max = p_max if p_max <= right_min else right_max

            next_right_min = min(p_max, right_min)
            for i in range(pivot_index, r + 1):
                ans[i] = curr_max
                next_right_min = min(next_right_min, nums[i])

            if pivot_index == 0: return

            process(pivot_index - 1, next_right_min, curr_max)
            
        process(n - 1, math.inf, -math.inf)
        return ans