You process a stream of real-valued points on the one-dimensional target segment `[0, 50]`. Each arriving point `x` permanently contaminates the closed interval `[x - 0.5, x + 0.5]` (a length-1 region). Contamination never goes away, and the regions from different points may overlap. Implement `solution(points)` which receives the full sequence of points (as a list of doubles, in arrival order) and returns a list of booleans of the same length: the i-th boolean is `true` if and only if the entire target segment `[0, 50]` is fully contaminated after the first `i+1` points have been processed. **Notes** - Points may arrive in any order. - A point may be any real value; only the overlap of its interval with `[0, 50]` matters (points whose interval lies entirely outside `[0, 50]` change nothing). - Updates should be supported efficiently (amortized near-constant time per point), so merging intervals as they arrive is preferred over rescanning everything each time. In an interview this would be modeled as a stateful object whose update method takes one `double` and returns one `bool`; here the equivalent contract is a single function over the whole stream so the behavior after every point can be checked deterministically.