Statement

Dario is experimenting with a new kind of brackets: the quantum brackets. A quantum bracket is in a superposition of (meaning, being at the same time) open and closed, and will collapse to either option when observed. Dario is working with K kinds of quantum brackets and he managed to get a sequence of N of those. He is wondering whether there exists a way in which they can collapse (meaning, become definitely open or closed) to form a well-parenthesized expression. An expression of K kinds of brackets is well-parenthesized if it is possible to one-to-one match each bracket with one of the same kind such that the first is open, the second is closed and taken any two intervals between matched brackets they are either disjoint or contained in one another.